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 ∠F?
Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees:
∠D + ∠E = 180
(4x + 8) + (x + 17) = 180
5x + 25 = 180
5x = 180 - 25
5x = 155
x = 155/5
x = 31
Now, we can find the measure of ∠D:
m ∠D = 4x + 8
m ∠D = 4(31) + 8
m ∠D = 124 + 8
m ∠D = 132
Since ∠F is a vertical angle of ∠D, the measure of ∠F is also 132 degrees. Answer: \boxed{132}.