Chapter 6.4, Problem 52STP

To determine

The measure of angle APB.

Answer to Problem 52STP

  $m\angle APB=112$

Explanation of Solution

Given:

The given figure is:

Calculation:

ABCD is a parallelogram because it has 2 pairs of congruent sides.

As the measure of angle BAD is a right angle, ABCD is a rectangle.

The diagonals of a rectangle are congruent and also bisect one another. Therefore, triangle PAD is an isosceles triangle and hence, $m\angle PAD=m\angle PDA.$

The measure of the exterior angle of a triangle equals to the sum of the measures of two remote interior angles.

So,

  $\begin{array}{l}m\angle PAD+m\angle PDA=m\angle APB\\ 56+56=m\angle APB\\ m\angle APB=112\end{array}$