Chapter 9.5, Problem 1WE

To determine

To find: the values of $x,y$ and $z$ .

Answer to Problem 1WE

The angles are as follows:

  $\begin{array}{l}x=30°\\ y=15°\\ z=25°\end{array}$

Explanation of Solution

Given information:

In the diagrams that follow, $O$ is the center of the circle.

Calculation:

The measure of an inscribed angle is equal to half the measure of its intercepted arc.

Consider the following figure,

As $AB$ is the diameter of $\odot O$ .

  $\begin{array}{c}arc\left(AB\right)=180°\\ 100°+x°+50°=180°\end{array}$

Therefore, the angles are as follows:

  $\begin{array}{l}x=30°\\ y=15°\\ z=25°\end{array}$