Chapter 6.4, Problem 18PPS

To determine

The measure of angle YXZ.

Answer to Problem 18PPS

  $m\angle YXZ=48$

Explanation of Solution

Given:

WXYZ is a rectangle.

  $m\angle XZY=3x+6\text{ and m}\angle XZW\text{ = 5x - 12}\text{.}$

Calculation:

A parallelogram that is a rectangle has 4 right angles.

Hence, measure of angle YZW is 90 degrees.

So,

  $\begin{array}{l}m\angle YZX+m\angle XZW=m\angle YZW\\ \left(3x+6\right)+\left(5x-12\right)=90\\ 8x-6=90\\ 8x=96\\ x=12\end{array}$

Hence, the measure of angle XZW will be:

  $\begin{array}{l}m\angle XZW=5x-12\\ m\angle XZW=5\left(12\right)-12\\ m\angle XZW=48\end{array}$

According to the definition of rectangle, $\overline{ZW}\parallel \overline{YX}$ .

So,

  $\begin{array}{l}m\angle YXZ=m\angle XZW\\ m\angle YXZ=48\end{array}$