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Center of rotation stays fixed · 10 practice problems

4.MD.C.5

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: (B) - rotated clockwise through the largest angle (210 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 30, (B) 210, (C) 150 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 30 degrees in (A), 210 degrees in (B), and 150 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=30∘\text{(A)} = 30^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=210∘\text{(B)} = 210^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=150∘\text{(C)} = 150^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 30, (B) 210, (C) 150 degrees. The largest is (B).
210∘>150∘>30∘210^\circ > 150^\circ > 30^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (B) - rotated clockwise through the largest angle (210 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (B) has the biggest measured turn (210 degrees), so naming (B) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (B) used the biggest angle!
Variant 2 answer: (C) - rotated clockwise through the largest angle (315 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 180, (B) 90, (C) 315 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 180 degrees in (A), 90 degrees in (B), and 315 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=180∘\text{(A)} = 180^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=90∘\text{(B)} = 90^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=315∘\text{(C)} = 315^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 180, (B) 90, (C) 315 degrees. The largest is (C).
315∘>180∘>90∘315^\circ > 180^\circ > 90^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (C) - rotated clockwise through the largest angle (315 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (C) has the biggest measured turn (315 degrees), so naming (C) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!
Variant 3 answer: (C) - rotated clockwise through the largest angle (225 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 90, (B) 180, (C) 225 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 90 degrees in (A), 180 degrees in (B), and 225 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=90∘\text{(A)} = 90^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=180∘\text{(B)} = 180^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=225∘\text{(C)} = 225^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 90, (B) 180, (C) 225 degrees. The largest is (C).
225∘>180∘>90∘225^\circ > 180^\circ > 90^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (C) - rotated clockwise through the largest angle (225 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (C) has the biggest measured turn (225 degrees), so naming (C) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!
Variant 4 answer: (A) - rotated clockwise through the largest angle (200 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 200, (B) 100, (C) 50 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 200 degrees in (A), 100 degrees in (B), and 50 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=200∘\text{(A)} = 200^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=100∘\text{(B)} = 100^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=50∘\text{(C)} = 50^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 200, (B) 100, (C) 50 degrees. The largest is (A).
200∘>100∘>50∘200^\circ > 100^\circ > 50^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (A) - rotated clockwise through the largest angle (200 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (A) has the biggest measured turn (200 degrees), so naming (A) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (A) used the biggest angle!
Variant 5 answer: (C) - rotated clockwise through the largest angle (270 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 60, (B) 150, (C) 270 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 60 degrees in (A), 150 degrees in (B), and 270 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=60∘\text{(A)} = 60^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=150∘\text{(B)} = 150^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=270∘\text{(C)} = 270^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 60, (B) 150, (C) 270 degrees. The largest is (C).
270∘>150∘>60∘270^\circ > 150^\circ > 60^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (C) - rotated clockwise through the largest angle (270 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (C) has the biggest measured turn (270 degrees), so naming (C) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!
Variant 6 answer: (C) - rotated clockwise through the largest angle (330 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 110, (B) 220, (C) 330 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 110 degrees in (A), 220 degrees in (B), and 330 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=110∘\text{(A)} = 110^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=220∘\text{(B)} = 220^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=330∘\text{(C)} = 330^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 110, (B) 220, (C) 330 degrees. The largest is (C).
330∘>220∘>110∘330^\circ > 220^\circ > 110^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (C) - rotated clockwise through the largest angle (330 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (C) has the biggest measured turn (330 degrees), so naming (C) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!
Variant 7 answer: (C) - rotated clockwise through the largest angle (255 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 75, (B) 165, (C) 255 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 75 degrees in (A), 165 degrees in (B), and 255 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=75∘\text{(A)} = 75^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=165∘\text{(B)} = 165^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=255∘\text{(C)} = 255^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 75, (B) 165, (C) 255 degrees. The largest is (C).
255∘>165∘>75∘255^\circ > 165^\circ > 75^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (C) - rotated clockwise through the largest angle (255 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (C) has the biggest measured turn (255 degrees), so naming (C) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!
Variant 8 answer: (C) - rotated clockwise through the largest angle (300 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 45, (B) 135, (C) 300 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 45 degrees in (A), 135 degrees in (B), and 300 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=45∘\text{(A)} = 45^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=135∘\text{(B)} = 135^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=300∘\text{(C)} = 300^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 45, (B) 135, (C) 300 degrees. The largest is (C).
300∘>135∘>45∘300^\circ > 135^\circ > 45^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (C) - rotated clockwise through the largest angle (300 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (C) has the biggest measured turn (300 degrees), so naming (C) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!
Variant 9 answer: (C) - rotated clockwise through the largest angle (240 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 120, (B) 90, (C) 240 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 120 degrees in (A), 90 degrees in (B), and 240 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=120∘\text{(A)} = 120^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=90∘\text{(B)} = 90^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=240∘\text{(C)} = 240^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 120, (B) 90, (C) 240 degrees. The largest is (C).
240∘>120∘>90∘240^\circ > 120^\circ > 90^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (C) - rotated clockwise through the largest angle (240 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (C) has the biggest measured turn (240 degrees), so naming (C) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!
Variant 10 answer: (B) - rotated clockwise through the largest angle (270 degrees).

Each green figure was made by rotating the orange figure clockwise about the red point. Write the label of the figure that was rotated through the largest angle. (The angle of rotation is greater than 0°0\degree and less than 360°360\degree.)

There are three cases, (A), (B), and (C). In each case the orange figure and the green figure meet at a single red point, which is the shared vertex. The green figure is obtained by rotating the orange figure clockwise about that red point.

  • In (A), the green figure was rotated clockwise by [ ].
  • In (B), the green figure was rotated clockwise by [ ].
  • In (C), the green figure was rotated clockwise by [ ].

Therefore, the figure rotated clockwise through the largest angle is [ ].

(A) (B) (C)
Show solution

Understand

In three cases (A), (B), (C), a green figure is made by rotating an orange figure clockwise about a shared red pivot point. The rotation angles are (A) 90, (B) 270, (C) 135 degrees. Name the case rotated through the largest angle.

Givens
  • Each case has an orange figure and a green copy meeting at a red pivot point (the center of rotation, which stays fixed).
  • The green figure is the orange figure rotated clockwise about the red point.
  • The clockwise turn is 90 degrees in (A), 270 degrees in (B), and 135 degrees in (C).
Unknowns
  • Which case used the largest rotation angle.
Constraints
  • Each rotation angle is greater than 0 degrees and less than 360 degrees.
  • The red pivot point does not move.

Plan

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships#3 Eliminate Possibilities

Each angle is found by drawing the ray from the pivot along a matching feature of the orange figure and of the green figure, then measuring the clockwise turn between them on the grid. Comparing the three measured angles identifies the largest. (Tool 3 is used on the genuinely finite set of three labeled cases, not on answer choices.)

Execute

#1 Draw a Diagram 4.MD.C.5
Pick a matching arm on the orange and green figures and read the clockwise turn between them at the red pivot.
(A)=90∘\text{(A)} = 90^\circ
The arm swings clockwise from its orange position to its green position.
#1 Draw a Diagram 4.MD.C.5
Do the same in (B): measure the clockwise turn of the matching arm at the pivot.
(B)=270∘\text{(B)} = 270^\circ
A bigger swing means a bigger rotation angle.
#17 Visualize Spatial Relationships 4.MD.C.5
Measure the clockwise turn of the matching arm in (C) at the pivot.
(C)=135∘\text{(C)} = 135^\circ
The slant of the green figure shows how far it swung around the pivot.
#3 Eliminate Possibilities 4.MD.C.5
Compare the three clockwise angles: (A) 90, (B) 270, (C) 135 degrees. The largest is (B).
270∘>135∘>90∘270^\circ > 135^\circ > 90^\circ
The figure swung furthest around the pivot was turned through the largest angle.
Answer: (B) - rotated clockwise through the largest angle (270 degrees).

Review

All three angles lie strictly between 0 and 360 degrees as required, and (B) has the biggest measured turn (270 degrees), so naming (B) as the largest is consistent with the picture.

Create a physical representation (tool 10): pin a tracing of each orange figure at the red point and rotate it clockwise until it lands on the green figure; the case needing the most turning is the largest angle.

Standards · min grade 4

  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Reading and comparing rotation angles formed at the shared pivot point in each case.
💡 Match an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (B) used the biggest angle!