Chapter 9, Problem 20CR

To determine

To complete: the blank in the given statement.

Explanation of Solution

Given information:

The given statement is “If arc length $EG=100$ and arc length $DF=40$ , then $m\angle EPG=$$\underset{\_}{}$ ”.

  $\overleftrightarrow{RS}$ is tangent to circle $N$

The given figure is as follows:

  

From the given diagram,

  $\begin{array}{l}m\angle EPG=\frac{1}{2}m(EG)-\frac{1}{2}m(DF)\\ =\frac{1}{2}(100-40)\\ ={30}^0\end{array}$

Hence, $m\angle EPG={30}^0$ .