Chapter 9.6, Problem 4CE

To determine

To find: find the measure of numbered angle

Answer to Problem 4CE

The measure of angle $\angle 4$ is $80°$

Explanation of Solution

Given information: we have given the figure of circle

  

As we know

The measure of an angle formed by the two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.

Therefore from given figure we must have

  $\begin{array}{c}\angle 4=\frac{1}{2}\left\{260°-\left(360°-260°\right)\right\}\\ =\frac{1}{2}\left\{260°-100°\right\}\\ =\frac{1}{2}\times 160°\\ =80°\end{array}$

Therefore, the measure of the angle $\angle 4$ is $80°$