Chapter 10.5, Problem 9PSA

To determine

To Find : $\text{Measure of}\stackrel{⌢}{CD}$

Answer to Problem 9PSA

  ${10}^{\circ }$

Explanation of Solution

Given Information :

  1) $\angle AEB={30}^{\circ }$

  2) $\stackrel{⌢}{AB}={50}^{\circ }$

Formula Used :

  $\frac{1}{2}\left(s_1+s_2\right)=\theta$ (angle between chords)

Calculation :

  $\begin{array}{l}\frac{1}{2}\left(\stackrel{⌢}{AB}+\stackrel{⌢}{CD}\right)=\angle AEB\\ \frac{1}{2}\left({50}^{\circ }+\stackrel{⌢}{CD}\right)={30}^{\circ }\\ {50}^{\circ }+\stackrel{⌢}{CD}={60}^{\circ }\\ \stackrel{⌢}{CD}={10}^{\circ }\end{array}$