If there are two supplementary angles, ∠D

Question

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

31°
31 degrees

48°
48 degrees

132°
132 degrees

124°

Answer 1

To find the measure of ∠F, we need to first find the value of x. Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees:

(4x + 8) + (x + 17) = 180

Combine like terms:

5x + 25 = 180

Subtract 25 from both sides:

5x = 155

Divide both sides by 5:

x = 31

Now that we have the value of x, we can find the measure of ∠D and ∠E:

m∠D = (4x + 8) = (4*31 + 8) = 132 degrees
m∠E = (x + 17) = (31 + 17) = 48 degrees

Since ∠F is a vertical angle with ∠D, it will have the same measure as ∠D. Therefore, the measure of ∠F is 132 degrees.

Answer: 132°

Answer 2

are you shure

Answer 3

Yes, I am sure. The measure of ∠F is 132 degrees.