Chapter 12, Problem 31CR

To determine

To calculate: The measure ofangle WYA.

Answer to Problem 31CR

The measure of angle WYA is $35°$ .

Explanation of Solution

Given information:

  $\begin{array}{l}\angle W=4x°\\ \angle A=x+45°\\ \angle Y=8x-{15}^{\circ }\end{array}$

Calculation:

  

  $\begin{array}{l}8x-{15}^{\circ }=4x+x+{45}^{\circ }\\ 8x=5x+{60}^{\circ }\\ 3x={60}^{\circ }\\ x=\frac{{60}^{\circ }}{3}={20}^{\circ }\end{array}$

  $\begin{array}{l}\angle AWY=4x°=\left(4\times {20}^{\circ }\right)={80}^{\circ }\\ \angle WAY=x+45°={20}^{\circ }+45°=65°\\ \angle Y=8x-{15}^{\circ }=\left(8\times {20}^{\circ }\right)-{15}^{\circ }={160}^{\circ }-{15}^{\circ }={145}^{\circ }\\ \angle WYA={180}^{\circ }-{145}^{\circ }={35}^{\circ }\end{array}$