Chapter 9.5, Problem 4WE

To determine

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

Answer to Problem 4WE

The angles are as follows:

  $\begin{array}{l}x=70°\\ y=110°\\ z=110°\end{array}$

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.

Consider the following figure,

Therefore, angle $x$ is equal to,

  $\begin{array}{c}x=\frac{140°}{2}\\ =70°\end{array}$

Further, the angle $y$ is equal to,

  $\begin{array}{c}y=55°\times 2\\ =110°\end{array}$

And angle $z$ is equal to,

  $\begin{array}{c}z=360°-\left(140°+y°\right)\\ =360°-250°\\ =110°\end{array}$

The angles are as follows:

  $\begin{array}{l}x=70°\\ y=110°\\ z=110°\end{array}$