We want the degree measure of angle APB. If we draw a perpendicular from point P to side
AB of the rectangle and call the point where the perpendicular drawn from point P to side AB
meets side AB point Q, then we will obtain two identical right triangles, triangles AQP and
BQP.
Point Q bisects AB. So the length of . Point P is the point of intersection of the
diagonals, so point P is the midpoint of both diagonals. Therefore . Now
angle APQ is of angle APB, whose degree measure we are seeking. Let’s find the degree
measure of angle APQ. Then we will take twice this number for the degree measure of angle
APB.
If we refer to angle APQ by the letter θ, then we have that