Geometry

Question Analysis

This question involves the Outside Angle Theorem. We are given the measure of an angle formed by two secants (or a secant and a tangent - like situation here) from an external point  to the circle and the measure of one intercepted arc . The goal is to find the measure of the other intercepted arc .

 

Key Concept Explanation

Outside Angle Theorem: The measure of an angle formed by two secants, two tangents, or a secant and a tangent from an external point to a circle is equal to half the difference of the measures of the intercepted arcs. If the angle is , the major arc is , and the minor arc is , then .

 

Step - by - Step Solution

1. Let the measure of minor arc  be .

The measure of the major arc  is , and the measure of .

2. Apply the Outside Angle Theorem:

According to the theorem,