Geometry

Question Analysis

This question focuses on applying the Outside Angle Theorem. We are given the measure of a major arc  and a minor arc  intercepted by a tangent  and a secant from an external point . The goal is to find the measure of  using the relationship between the angle and the intercepted arcs.

 

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. First, find the measure of minor arc :

The sum of arc measures in a circle is . Given arc  and arc , then the measure of minor arc

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