Geometry

Question Analysis

The main focus is to use the Outside Angle Theorem for angles formed by two tangents from an external point to a circle. We need to set up an equation based on the relationship between the given angle and the intercepted arcs to solve for .

 

Key Concept Explanation

Outside Angle Theorem for Two Tangents: When two tangents are drawn from an external point to a circle, the measure of the angle formed is half the difference of the measures of the intercepted arcs. The sum of the measures of the major and minor intercepted arcs is . If the angle is , the major arc is , and the minor arc is , then , and , so .

 

Step - by - Step Solution

1. Determine the arc measures:

The measure of the major arc is , so the measure of the minor arc is .

2. Apply the Outside Angle Theorem:

According to the theorem,

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