Problem
The four inside angles add to 360 degrees, so subtract the three known angles.
The full set of quadrilateral corners is fixed at 360, so the unknown corner is whatever is left.
4.MD.C.7Identify SubproblemsThe bottom inside angle b is what remains when the three known corners (100 degrees, 80 degrees, 70 degrees) are taken away from the quadrilateral's total of 360 degrees.
A quadrilateral's four inside angles always add up to 360 degrees, so the three known corners together with b must fill exactly 360 degrees.
Drawing one diagonal cuts the quadrilateral into two triangles whose corners are exactly the quadrilateral's four corners, with nothing left out and nothing counted twice.
Each of those two triangles has three corners that add to 180 degrees, and 180 degrees and 180 degrees together make 360 degrees.
Because the four corners have a fixed total of 360 degrees, taking the three known corners away from 360 degrees leaves exactly the one corner b that was missing.
The total 360 degrees was built by adding the four corners, and subtraction undoes that adding to pull back out the part we did not yet know.
The three angles 45 degrees, b = 110 degrees, and a lie along the straight line and add to 180 degrees. Subtract the two known ones.
The flat line is 180 degrees split into three pieces; the last piece is the remainder.
4.MD.C.7Identify SubproblemsFirst the 360-degree rule gives the missing corner, then the 180-degree straight line gives angle a - two friendly Grade 4 subtractions!