Question

If there are two supplementary angles, ∠D

and ∠E
, where m∠D=(4x+8)° and m∠E=(x+17)° , and ∠F is a vertical angle with ∠D , what is the measure of ∠F ?



(1 point)
Responses

132°
132 degrees

124°
124 degrees

48°
48 degrees

31°

Answer 1

[AI-generated answer — Bot GPT 3.5]

The measure of ∠F will be equal to the measure of ∠E, since they are vertical angles.

Therefore, ∠F = ∠E = (x+17)°.

Since ∠D and ∠E are supplementary angles, their measures add up to 180°.
So, we can write the equation: (4x+8)° + (x+17)° = 180°.

Simplifying this equation, we get:
5x + 25 = 180
5x = 180 - 25
5x = 155
x = 155/5
x = 31

Substituting this value back into ∠F = (x+17)°, we get:
∠F = 31 + 17
∠F = 48°

Therefore, the measure of ∠F is 48 degrees. Answer: 48°.