Chapter 9.5, Problem 5WE

To determine

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

Answer to Problem 5WE

The angles are as follows:

  $\begin{array}{l}x=50°\\ y=130°\\ z=65°\end{array}$

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.

Also,

Consider the following theorem:

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

Hence, the angle $x$ is equal to $x=50°$ .

As the triangle is isosceles, $z°=2y°$ ,

By angle sum property,

  $\begin{array}{c}50°+z°+z°=180°\\ z°=65°\end{array}$

Further, angle $y$ is equal to,

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

The angles are as follows:

  $\begin{array}{l}x=50°\\ y=130°\\ z=65°\end{array}$