Chapter 8.7, Problem 57SPR

To determine

To calculate:

The value of $m\angle 12$ in a quadrilateral $WXYZ$

Answer to Problem 57SPR

The value of $m\angle 12$ is $120$ 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:

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

In $\Delta WAX$ ,

Triangle ange-sum theorem shows:

  $\begin{array}{l}m\angle 11=180-m\angle 8-m\angle 1\\ m\angle 11=180-30-30\\ m\angle 11=120\end{array}$

The theorem of vertical angles:

  $\begin{array}{l}m\angle 12=m\angle 11\\ m\angle 12=120\end{array}$

Hence, the value of $m\angle 12$ is $120$ in a quadrilateral $WXYZ$ .