Geometry

Question Analysis

This question focuses on applying the Outside Angle Theorem. We need to first correctly determine the measure of the major arc intercepted by the tangent  and the secant, and then use the theorem to find the measure of .

 

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. Find the measure of arc :

Since the sum of arc measures in a circle is , and we know arc  and part of the other arc is , then the measure of arc .

2. Apply the Outside Angle Theorem:

Let the major arc

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