Chapter 9.5, Problem 3WE

To determine

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

Answer to Problem 3WE

The angles are as follows:

  $\begin{array}{l}x=110°\\ y=100°\\ z=100°\end{array}$

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, if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

  $\begin{array}{c}x=180°-70°\\ =110°\\ y=180°-80°\\ =100°\end{array}$

Consider the following figure,

From the figure, the measure of given inscribed angle is exactly half the measure of its intercepted arc.

  $\begin{array}{c}x=60°+\frac{z°}{2}\\ z=2\times \left(110°-60°\right)\\ =100°\end{array}$

The angles are as follows:

  $\begin{array}{l}x=110°\\ y=100°\\ z=100°\end{array}$