Chapter 9.5, Problem 2WE

To determine

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

Answer to Problem 2WE

The angles are as follows:

  $\begin{array}{l}x=130°\\ y=120°\\ z=110°\end{array}$

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,

Therefore, values of angles $x$ and $y$ are as follows;

  $\begin{array}{c}y=2\times 60°\\ =120°\\ x=2\times 65°\\ =130°\end{array}$

Value of angle $z$ is as follows:

  $\begin{array}{c}z=360°-\left(x+y\right)\\ =360°-250°\\ =110°\end{array}$

So, the angles are,

  $\begin{array}{l}x=130°\\ y=120°\\ z=110°\end{array}$