Chapter 9.5, Problem 9CE

To determine

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

Answer to Problem 9CE

The measure of the angles is;

  $x=y=70°$

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.

Since, $NX=NY$

Angle opposite to equal sides is equal,

Also,

  $\begin{array}{c}\angle N=\frac{80°}{2}\\ =40°\end{array}$

By angle sum property,

The sum of angles in a triangle is,

  $\begin{array}{c}x+y+N=180°\\ 2x+40°=180°\\ x=70°\end{array}$

Therefore, the values of the angles are,

  $x=y=70°$