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 ∠KML.

 

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. The equal - length markings from  to  and  to  imply that  bisects ∠NML. So, ∠KMN = ∠KML.

 

Step - by - Step Solution

1. Since  bisects ∠NML, by the Angle Bisector Equidistant Theorem, ∠KMN = ∠KML.

We know that ∠KMN=(2x + 65)° and ∠KML=(8x + 35)°. So, we set up the equation .

Subtract  from both sides: