Geometry

Question Analysis

The main focus is using the markings in the diagram and the Angle Bisector Equidistant Theorem to determine the measure of ∠YXZ.

Key Concept Explanation

The Angle Bisector Equidistant Theorem states that if a point lies on the angle bisector of an angle, it is equidistant from the two sides of the angle. Conversely, if a point is equidistant from the two sides of an angle, it lies on the angle bisector. Equal - length markings on perpendicular segments from a point to the sides of an angle can help identify an angle bisector.

Step - by - Step Solution

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

By the converse of the Angle Bisector Equidistant Theorem, since the distances from point  to the two sides of the angle at

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