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 132° 132 , 31 31, 124 124
If ∠D and ∠E are supplementary angles, their sum is 180°.
So, (4x+8) + (x+17) = 180.
Combining like terms, we get 5x + 25 = 180.
Subtracting 25 from both sides, we get 5x = 155.
Dividing both sides by 5, we get x = 31.
Substituting x = 31 into the expression for ∠D, we get ∠D = (4(31) + 8) = 132°.
Since ∠F is a vertical angle with ∠D, ∠F has the same measure as ∠D.
Therefore, the measure of ∠F is 132°.
The correct answer is 132°.