Chapter 9.5, Problem 7CE

To determine

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

Answer to Problem 7CE

The measure of the angles is;

  $\begin{array}{l}x=70°\\ y=95°\end{array}$

Explanation of Solution

Given information:

Given figure,

  $O$ is the center of the circle.

Calculation:

Consider the theorem:

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

Thus,

  $\begin{array}{c}\frac{x}{2}=60°\\ x=120°\end{array}$

And,

  $\begin{array}{l}y=\frac{x}{2}\\ y=60°\end{array}$

Therefore, the measures of the angles are,

  $\begin{array}{l}x=120°\\ y=60°\end{array}$