Geometry

Question Analysis

The main focus is on applying the property of inscribed angles. We need to find the measure of the arc intercepted by ∠LMN and then use the rule that an inscribed angle is half the measure of its intercepted arc to determine .

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. First, find the measure of the arc intercepted by ∠LMN.

The total degrees in a circle is . Given arcs are  and .

The measure of the intercepted arc is

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