Geometry

Question Analysis

This question focuses on applying the Outside Angle Theorem. We are given the measure of an angle formed by two secants 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,