Question

PLease help me. 1. If m DEF= 129, then what are m FEG and m HEG?

Answer 1

Answer:

$m\angle HEG=129^{\circ}$

$m\angle FEG=51^{\circ}$

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle FEG and angle HEG.

We can see that angle DEF and HEG are vertical angles, so measure of both angles will be equal.

$m\angle HEG=m\angle DEF$

$m\angle HEG=129^{\circ}$

Therefore, the measure of angle HEG is 129 degrees.

We can also see that angle HEG and FEG is a linear pair of angles, so they will add up-to 180 degrees.

$m\angle HEG+m\angle FEG=180^{\circ}$

$129^{\circ}+m\angle FEG=180^{\circ}$

$129^{\circ}-129^{\circ}+m\angle FEG=180^{\circ}-129^{\circ}$

$m\angle FEG=51^{\circ}$

Therefore, the measure of angle FEG is 51 degrees.

Answer 2

For this case we have that the sum of the angles DEF and FEG is equal to 180 degrees.

Therefore, we have:

$DEF + FEG = 180$

From here, we clear the FEG angle.

We have then:

FEG = 180 - DEF

Substituting values we have:

FEG = 180 - 129

FEG = 51

Then, on the other hand we have that the sum of the angles FEG and HEG is equal to 180 degrees.

Therefore, we have:

HEG + FEG = 180

From here, we clear the HEG angle:

HEG = 180 - FEG

Substituting values we have:

HEG = 180 - 51

HEG = 129

Answer:

The values of HEG and FEG are:

FEG = 51

HEG = 129