If there are 2 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. 132°
B. 124°
C. 31°
D. 48°
Since angles D and E are supplementary, their measures add up to 180°:
m D + m E = 180°
(4x + 8)° + (x + 17)° = 180°
5x + 25° = 180°
5x = 155°
x = 31°
To find the measure of angle F, we need to find the measure of angle D:
m D = (4x + 8)°
m D = (4(31) + 8)°
m D = 124°
Since F is a vertical angle with D, the measure of angle F is also 124°.
Therefore, the answer is B. 124°.