Geometry

Question Analysis

The main focus is using the equal - length markings (suggesting is an angle - bisector) and the given angle expressions along with the Angle Bisector Equidistant Theorem to find the value of and then determine the measure of ∠LMN.

 

Key Concept Explanation

The Angle Bisector Equidistant Theorem states that if a ray bisects an angle, then any point on that ray is equidistant from the two sides of the angle. Here, the equal - length markings from to and to imply that bisects ∠NML. So, ∠NMK = ∠LMK.

 

Step - by - Step Solution

1. Since bisects ∠NML, by the Angle Bisector Equidistant Theorem, ∠NMK = ∠LMK.

We know that ∠NMK=(x + 22)° and ∠LMK=(3x - 34)°. So, we set up the equation .

Subtract

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