Geometry

Question Analysis

This question focuses on using the Outside Angle Theorem for circles. We are given the measure of the major arc intercepted by two tangents and need to find the measure of the angle formed by the tangents outside the circle.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Find the measure of the minor arc:

The measure of the major arc . Since the sum of the major and minor arcs is , the measure of the minor arc .

2. Apply the Outside Angle Theorem:

Substitute  and

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