Geometry

Question Analysis

The main focus is on the relationship between central angles and inscribed angles that intercept the same arc. We know the measure of the central angle , and we need to find the measure of the inscribed angle that intercepts the same arc .

 

Key Concept Explanation

A central angle has its vertex at the center of the circle, and an inscribed angle has its vertex on the circle. The measure of an inscribed angle that intercepts the same arc as a central angle is half of the measure of the central angle.

 

Step - by - Step Solution

1. We are given that the measure of the central angle .

2. The inscribed angle intercepts the same arc as the central angle .

3. According to the property, the measure of an inscribed angle is half of the measure of the central angle that intercepts the same arc. So,

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