Chapter 6.4, Problem 30PPS

To determine

The measure of angle 6.

Answer to Problem 30PPS

  $m\angle 6=50$

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, $\angle 2\cong \angle CBA.$

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

A rectangle has 4 right angles.

So, angle ABD is a right angle.

Therefore,

  $\begin{array}{l}m\angle CBA+m\angle 6=m\angle ABD\\ 40+m\angle 6=90\\ m\angle 6=50\end{array}$