Geometry

Question Analysis

The main focus is using the equal - length markings (indicating  is likely 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 ∠TRU.

 

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  suggest that  bisects ∠URS. So, ∠TRU = ∠TRS.

 

Step - by - Step Solution

1. Since  bisects ∠URS (implied by the markings), by the Angle Bisector Equidistant Theorem, ∠TRU = ∠TRS.

We know that ∠TRU=(8x - 20)° and ∠TRS=(6x)°. So, we set up the equation .

Subtract  from both sides: , which simplifies to

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