Chapter 13, Problem 7STP

To determine

Find $m\angle S$ .

Answer to Problem 7STP

  $m\angle S=77°$

Explanation of Solution

Given:

Formula Used:

Outside Angle Theorem :

The measure of an angle formed by two tangents drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Calculation:

First we find the measure of intercepted arcs.

Measure of one intersepted arc is $103°$ and the measure of other intercepted angle is $360°-103°$

So, $m\angle RST=\frac{\left(180°-103°\right)-103°}{2}=\frac{154}{2}=77°$

Hence, $m\angle S=77°$