Question

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

Answer 1

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.