Geometry

Question Analysis

The main focus is correctly applying the Tangent - chord theorem. We first need to determine the correct arc measure based on the given angle between the tangent and the chord . Then, we use the relationship between the minor and major arcs to set up an equation and solve for .

 

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. Given that 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's measure is