Chapter 8.7, Problem 56SPR

To determine

To calculate:

The value of $m\angle 8$ in a quadrilateral $WXYZ$

Answer to Problem 56SPR

The value of $m\angle 8$ is $30$ in a quadrilateral $WXYZ$ .

Explanation of Solution

Given information:

  

  $m\angle 1=30$

Calculation:

  

From Figure, know that the two diagonal of rectangle are congruent, and bisect to each other.

  $\Delta AWX$ is isosceles with $AW=AX$ .

Theorem of isosceles theorem:

  $\begin{array}{l}m\angle 8=m\angle 1\\ m\angle 8=30\end{array}$

Hence, the value of $m\angle 8$ is $30$ in a quadrilateral $WXYZ$ .