Chapter 9.5, Problem 6CE

To determine

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

Answer to Problem 6CE

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.

The measure of each inscribed angles is exactly half the measure of its intercepted arc.

Hence,

  $\begin{array}{c}x+110°=180°\\ x=180°-110°\\ =70°\end{array}$

And,

  $\begin{array}{c}y+85°=180°\\ y=180°-85°\\ y=95°\end{array}$

Therefore, the measures of the angles are,

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