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
31°
31 degrees
48°
48 degrees
132°
132 degrees
124°
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°