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 ∠ZXY.

 

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 ∠WXY. So, ∠ZXW = ∠ZXY.

 

Step - by - Step Solution

1. Since  bisects ∠WXY, by the Angle Bisector Equidistant Theorem, ∠ZXW = ∠ZXY.

We know that ∠ZXW=(3x - 17)° and ∠ZXY=(4x - 38)°. So, we set up the equation .

Subtract  from both sides: