Question

Use the figure below to identify angles and segment lengths

Answer 1

So Angle GEN and FED are vertical angles, which means that their angles are congruent. Therefore, Angle FED is 60°

Angle GEN and DEN are a linear pair, which means that they are supplementary angles (add up to 180). To find Angle DEN, we have to form the equation: 60 + DEN = 180

For this, all you have to do is subtract 60 on both sides, and your answer will be: DEN = 120°

Answer 2

m∠FED = 60° and m∠DEN = 120°

Explanation:

In the figure attached,

Line segments FN and GD intersect each other at a point E forming an angle GEN = 60°

Since ∠FED ≅ ∠GEN ≅ 60° [Vertically opposite angles]

∠FED and ∠DEN are linear pairs on a line FN therefore,

m∠FED + m∠DEN = 180°

m∠DEN = 180 - m∠FED

= 180 - 60

= 120°

Therefore, m∠FED = 60° and m∠DEN = 120°