Chapter 9.3, Problem 10CE

To determine

To find: find the measure of central angle from the figure

Answer to Problem 10CE

The measure of angle $\angle$ GQE is $110°$

Explanation of Solution

Given information: we have given the figure of circle

  

Here, we can see that in the figure

  $\begin{array}{c}m\stackrel{⌢}{GE}=m\stackrel{⌢}{GF}+m\stackrel{⌢}{FE}\\ =60+50\\ =110°\end{array}$

As we know,

  $\begin{array}{c}m\angle GQE=m\stackrel{⌢}{GE}\\ =110°\end{array}$

Therefore, the measure of the angle $\angle$ GQE is $110°$