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?
A. 48
B. 124
C. 132
D. 31
Since D and E are supplementary angles, we can set up the equation:
mD + mE = 180
(4x + 8) + (x + 17) = 180
5x + 25 = 180
5x = 155
x = 31
Now we can find the measure of angle D:
mD = 4(31) + 8 = 132
Since F is a vertical angle with D, its measure is also 132.
Therefore, the measure of F is 132 degrees.
The answer is C. 132.