Geometry

Question Analysis

This question requires applying the Outside Angle Theorem. We know the measure of one arc and need to find the measure of another arc first to calculate the angle formed by a tangent and a secant from an external point.

 

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 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. Find the measure of arc :

Since the sum of arc measures in a circle is , and we know arc and arc , then the measure of arc .

2. Apply the Outside Angle Theorem:

Let the major arc

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