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° 31 degrees
If ∠D and ∠E are supplementary angles, it means that the sum of their measures is 180 degrees.
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 find that m∠D = (4(31)+8)° = 132°
Since ∠F is a vertical angle with ∠D, it will have the same measure.
Therefore, the measure of ∠F is 132°. Answer: $\boxed{132\text{ degrees}}$.