Reasoning · Grade 4-1 Polygons and Angles
Problem
The top line lets each given angle be renamed as an equal one.
A point sitting on a segment does not change the direction you are looking, so naming an angle by the near point or the far point on the same ray describes the very same angle.
4.G.A.1Draw A DiagramIn the big triangle the crossing angle is 100 degrees.
Triangle AGD is the one triangle that holds both of the top-line angles at once, so it is where the two givens can finally be combined.
8.G.A.5Identify SubproblemsTriangle AGD is the one triangle holding both given top-line angles, so it is where the two clues can finally be combined.
The three corners of any flat triangle always add to one straight angle, so two known corners hand over the third.
Because angle measures add, the two givens can be poured into one total and the remaining corner read off in one subtraction.
Swinging to the other side gives 80 degrees.
Flipping to the other side of a straight line is just one subtraction from 180°, and it moves the known angle to the side of G that faces F and B.
7.G.B.5Organize Information In More WaysThe next triangle gives the first answer, 76 degrees.
The 80° found at G and the 24° given at B are exactly the two corners of triangle FGB that are not the target, so one more triangle sum finishes the job.
8.G.A.5Identify SubproblemsThe second chase starts from 105 degrees.
The other two givens, 50° and 25°, sit together in triangle AEC, so it is the natural place to start the second chain.
8.G.A.5Identify SubproblemsIts neighbour is 75 degrees.
The needed angle at H opens toward D, so the measure at E has to be moved to the D side of the top line first — again a single subtraction from 180°.
7.G.B.5Organize Information In More WaysThe last triangle makes the second answer 75 degrees.
Triangle EHD hangs off the same top line as the first triangle, so the 30° given at D gets reused a second time and only one new angle had to be found.
8.G.A.5Identify SubproblemsIn a crowded figure, hunt for the one triangle that already holds two known angles — then pass its answer along to the next triangle like a relay baton.