Chapter 6.4, Problem 29PPS

To determine

The measure of angle 5.

Answer to Problem 29PPS

  $m\angle 5=80$

Explanation of Solution

Given:

ABCD is a rectangle.

  $m\angle 2=40$

Calculation:

The diagonals in a rectangle are congruent and bisect each other.

Therefore, triangle AEB is an isosceles triangle.

According to Isosceles Triangle Theorem, $\angle 2\cong \angle CBA.$

  $\begin{array}{l}m\angle CBA=m\angle 2\\ m\angle CBA=40\end{array}$

According to Exterior Angle Theorem, the measure of exterior angle of a triangle is equal to the sum of the measures of two remote interior angles.

So,

  $\begin{array}{l}m\angle 2+m\angle CBA=m\angle 5\\ 40+40=m\angle 5\\ m\angle 5=80\end{array}$