Geometry

Question Analysis

The main focus is using the markings indicating equal perpendicular distances (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 ∠FEG.

 

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 ∠FEH. So,  ∠HEG = ∠FEG.

 

Step - by - Step Solution

1. Since bisects ∠FEH, by the Angle Bisector Equidistant Theorem, ∠HEG = ∠FEG.

We know that ∠HEG=(9x + 9)° and ∠FEG=(6x + 21)°. So, we set up the equation .

Subtract from both sides: , which simplifies to

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