Geometry

Question Analysis

The main focus is using the markings and the given angle measure, along with the Angle Bisector Equidistant Theorem concept, to find the measure of ∠LMK.

Key Concept Explanation

The Angle Bisector Equidistant Theorem states that a point on an angle bisector is equidistant from the two sides of the angle. The converse is also true: if a point is equidistant from the two sides of an angle, it lies on the angle bisector. In geometric diagrams, equal - length markings can sometimes imply the existence of an angle bisector.

Step - by - Step Solution

1. Notice the equal - length markings on  and . Also,  and .

Since the distances from point  to the two sides of ∠NML are equal (because of the equal - length markings of the perpendicular segments

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