Geometry

Question Analysis

The main focus is using the relationship between inscribed angles and their intercepted arcs. Given the measure of an inscribed angle, we need to find the measure of the arc it intercepts.

 

Key Concept Explanation

An inscribed angle in a circle has its vertex on the circle and its sides as chords. The measure of an inscribed angle is half of the measure of the arc it intercepts.

 

Step - by - Step Solution

1. We know that the measure of inscribed angle .

2. By the inscribed - angle property, if  is the inscribed angle and  is the intercepted arc, then .

3. To find , we rearrange the formula:

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