Chapter 9.6, Problem 11WE

To determine

To find: find the measure of numbered angle

Answer to Problem 11WE

The measure of angle $\angle$ 1 is 60

Explanation of Solution

Given information: we have given $m\stackrel{⌢}{RT}$ =80, $m\stackrel{⌢}{US}$ =40 and 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

  $\begin{array}{c}m\angle 1=\frac{1}{2}\left(m\stackrel{⌢}{RT}+m\stackrel{⌢}{US}\right)\\ m\angle 1=\frac{1}{2}\left(80+40\right)\\ m\angle 1=\frac{120}{2}\\ m\angle 1=60\end{array}$

Therefore, the measure of the angle $\angle$ 1 is 60