Chapter 10.5, Problem 11PSA

To determine

To Find : $\text{Measure of}\stackrel{⌢}{XZ}$

Answer to Problem 11PSA

  ${81}^{\circ }$

Explanation of Solution

Given Information :

  1) $\angle Y={22}^{\circ }$

  2) $\stackrel{⌢}{WZ}={125}^{\circ }$

  3) $\overleftrightarrow{YZ}$ is tangent at $Z$

Formula Used: $\frac{1}{2}\left(s_1-s_2\right)=\theta$ (angle between secant and tangent)

Calculation :

  $\begin{array}{l}\frac{1}{2}\left(\stackrel{⌢}{WZ}-\stackrel{⌢}{XZ}\right)=\angle Y\\ \frac{1}{2}\left({125}^{\circ }-\stackrel{⌢}{XZ}\right)={22}^{\circ }\\ {125}^{\circ }-\stackrel{⌢}{XZ}={44}^{\circ }\\ \stackrel{⌢}{XZ}={81}^{\circ }\end{array}$