Problem
The four inside angles of a quadrilateral add to 360 degrees. Subtract the three known ones to get the bottom-left inside angle.
The whole turn around a quadrilateral's corners is fixed, so the leftover after removing three corners must be the fourth.
4.MD.C.7Identify SubproblemsThe bottom-left inside corner of the quadrilateral measures 110 degrees, found by taking the three known corners away from 360 degrees.
The four inside corners of any quadrilateral always add up to 360 degrees, so the three known corners and the bottom-left corner together must total 360.
A diagonal cuts the quadrilateral into two triangles, and those two triangles' corners are exactly the quadrilateral's four corners with nothing added and nothing left out.
Each of the two triangles has three angles that add to 180 degrees, so the two triangles supply 180 plus 180, which is 360.
The two triangles cover the whole quadrilateral with no gaps and no overlap, so their angles add back up to exactly the quadrilateral's angles.
Since the four corners add to a fixed 360 degrees, taking the three known corners away from 360 leaves exactly the one bottom-left corner.
Piling the corners together and taking them away are opposite moves, so subtraction gives back the single corner that was not told to us.
At the bottom-left corner, 110 degrees and the marked angle share the straight line, making 180 degrees.
A flat line is a straight angle of 180 degrees; the two angles on it must fill exactly that.
4.MD.C.7Identify SubproblemsFind the missing corner with the 360-degree rule, then take it away from the straight line's 180 degrees - just Grade 4 add-and-subtract-angles!