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 ∠POR.

 

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 ∠POR. So, ∠ROQ = ∠POQ.

 

Step - by - Step Solution

1. Since  bisects ∠POR, by the Angle Bisector Equidistant Theorem, ∠ROQ = ∠POQ.

We know that ∠ROQ=(4x - 15)° and ∠POQ=(x + 18)°. So, we set up the equation .

Subtract  from both sides:

Click "Show Answer" to reveal the answer and analysis