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

48°
48 degrees

124°
124 degrees

31°
31 degrees

132°
132 degrees
To find the measure of ∠F, we need to find the measure of ∠D. Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees:
m∠D + m∠E = 180
(4x+8) + (x+17) = 180
5x + 25 = 180
5x = 155
x = 31
Now we can find the measure of ∠D:
m∠D = (4x+8) = (4*31 + 8) = 132 degrees
Since ∠F is a vertical angle with ∠D, they have the same measure. Therefore,
m∠F = m∠D = 132 degrees
So the answer is 132°.