Geometry

Question Analysis

The main focus is on using the property of inscribed angles. An inscribed angle is half of the measure of the intercepted arc. We need to find the measure of the intercepted arc for ∠FEG and then apply this property to find its measure.

 

Key Concept Explanation

An inscribed angle in a circle is an angle whose vertex is on the circle and whose sides contain chords of the circle. The measure of an inscribed angle is always half of the measure of the arc that it intercepts.

 

Step - by - Step Solution

1. First, find the measure of the arc intercepted by ∠FEG. The total degrees in a circle is 360°. The two given arcs are 103° and 157°.

The measure of the arc intercepted by ∠FEG is .

2. Then, use the inscribed - angle property. Since the measure of an inscribed angle is half of the measure of the intercepted arc, for ∠FEG:

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