Chapter 6.5, Problem 57SPR

To determine

The measure of angle 6.

Answer to Problem 57SPR

  $m\angle 6=38$

Explanation of Solution

Given:

ABDC is a rectangle.

  $m\angle 1=38$

Calculation:

The diagonals of a rectangle are congruent and also bisect each other.

So, triangle AEC is an isosceles triangle.

According to Isosceles Triangle Theorem, $\angle 1\cong \angle ACB$ .

Also, according to the definition of a rectangle, $\overline{AC}\parallel \overline{BD}.$

Using Alternate Interior Angles Theorem; $\angle 6\cong \angle ACB.$

By Transitive Property of Congruence; $\angle 6\cong \angle 1$ .

So,

  $\begin{array}{l}m\angle 6=m\angle 1\\ m\angle 6=38\end{array}$