Chapter 9.3, Problem 13PSB

To determine

To find: The length of arc $m\stackrel{⌢}{EF}$ and also calculate the value of angle $\angle EDF$ .

Answer to Problem 13PSB

The length of the arc $m\stackrel{⌢}{EF}$ is ${60}^{\text{o}}$ and the value of the $\angle EDF$ is ${30}^{\text{o}}$

Explanation of Solution

Given information :

  $\begin{array}{l}\text{Measure of arc }FG=m\stackrel{⌢}{FG}={80}^{\text{o}}\\ \text{Measure of arc }DE=m\stackrel{⌢}{DE}={40}^{\text{o}}\end{array}$

Formula used :

  $\text{Measure of the arc}=\text{ Angle made by the arc at center of the circle}$

Since, angle formed by the radius is twice of the angle formed by the chords at the circumference of the circle.

Calculation :

The measure of arc $\stackrel{⌢}{EF}$

  $\begin{array}{l}={180}^{\text{o}}–\text{ (}m\stackrel{⌢}{FG}\text{ +}m\stackrel{⌢}{DE}\text{ )}\\ ={180}^{\text{o}}–\text{ (}{80}^{\text{o}}\text{ + }{40}^{\text{o}}\text{) }\\ \text{= }{180}^{\text{o}}-{120}^{\text{o}}={60}^{\text{o}}\end{array}$

And $\angle EDF=\frac{{60}^{\text{o}}}{2}={30}^{\text{o}}$