The complement of an angle is one-eight the measure of the supplement of the angle. What is the measure of the supplement angle to the nearest hundredth of a degree?
Responses
A 105.17°105.17°
B 99.13°99.13°
C 103.05°103.05°
D 102.86°102.86°
E 101.14°
Let the angle be x.
The complement of x is 90-x.
The supplement of x is 180-x.
According to the problem, 90-x = (1/8)(180-x).
Simplifying this equation:
720 - 8x = 180 - x
7x = 540
x = 77.14
So the supplement of x is 180-x = 102.86.
Therefore, the answer is D, 102.86° to the nearest hundredth of a degree.