Geometry

Question Analysis

The main focus is correctly applying the Tangent - chord theorem. We need to use the given angle between the tangent and the chord to find the measure of the intercepted arc, and then solve for using the expression for that arc.

 

Key Concept Explanation

Tangent - chord Theorem: The measure of the angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.

 

Step - by - Step Solution

1. The angle between the tangent and the chord is . Since this angle intercepts the major arc, by the Tangent - chord theorem, the measure of the major arc is .

2. The minor arc, whose measure is given by , and the major arc together make up a full - circle (). So we set up the equation

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