Geometry

Question Analysis

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

 

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  imply that  bisects ∠EFG. So, ∠EFH = ∠GFH.

 

Step - by - Step Solution

1. Since  bisects ∠EFG, by the Angle Bisector Equidistant Theorem, ∠EFH = ∠GFH.

We know that ∠EFH=(18x + 2)° and ∠GFH=(23x - 13)°. So, we set up the equation .

Subtract

Click "Show Answer" to reveal the answer and analysis