Angles my man, burn it to the ground!

b. Measure of Angle FEG = 70°, Measure of Angle HEG = 110°

Step-by-step explanation:

Angle FEG is adjacent and supplementary to the angle with the measure that we are given, Angle DEF, which measures 110 degrees.

We know that supplementary angles add up together to a total of 180 degrees.

So to find the measure of Angle FEG, we subtract the measure of Angle DEF from 180 degrees.

Measure of Angle FEG = 180 degrees - Measure of Angle DEF

Measure of Angle FEG = 180 degrees - 110 degrees

Measure of Angle FEG = 70 degrees

Angle HEG is a vertical angle to the angle that we are given, Angle DEF, which measure 110 degrees. Since vertical angles are congruent, we know that the measure of Angle HEG is equal to the measure of Angle DEF, so Angle HEG measures 110 degrees, also.

Measure of Angle HEG = Measure of Angle DEF

Measure of Angle HEG = 110 degrees

  or  

sin y = 7/q

7 is the opposite side length, q is the hypotenuse

tan y = 7/r

7 is the opposite side length, r is the adjacent side length

using sohcahtoa ^^^^

cos y = adjacent/hypotenuse

cos y = r/q