Geometry

Question Analysis

The main focus is correctly applying the Tangent - chord theorem. We need to identify the correct intercepted arc for the given angle between the tangent and the chord and then use the theorem to find the arc's measure.

 

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. Mathematically, if is the angle between the tangent and the chord, and is the measure of the intercepted arc, then .

 

Step - by - Step Solution

1. We are given that the angle between the tangent and the chord is .

2. According to the Tangent - chord theorem, to find the measure of the intercepted arc, we use the formula .

3. Substitute into the formula:

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