Chapter 9.5, Problem 8CE

To determine

To Find: The values of x and y for the given circle.

Answer to Problem 8CE

The values of $x$ is 65° and $y$ is 40°.

Explanation of Solution

Given information:

  

O is the center of the circle.

Consider the theorem:

The calculation of the inscribed angle is equal to half of the calculation of the arc that has been intercepted.

That is,

  $\begin{array}{l}\angle M=\frac{{150}^{\circ }}{2}\hfill \\ =75°\hfill \end{array}$

By angle sum property,

The sum of the angles of a triangle is

  $\begin{array}{l}\begin{array}{l}x+75°+40°=180°\hfill \\ x+115°=180°\hfill \end{array}\\ x=65°\end{array}$

Also,

  $\begin{array}{l}\stackrel{⌢}{MY}=2\times 40°\hfill \\ \stackrel{⌢}{MY}=80°\hfill \end{array}$

Hence, the value of the angle y is;

  $\begin{array}{l}y=\frac{1}{2}\times 80\hfill \\ y=40°\hfill \end{array}$

Therefore, the value of the angles is $x=65°$ and $y=40°$ .