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?

Question

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	102.86°102.86°
B	101.14°101.14°
C	105.17°105.17°
D	99.13°99.13°
E	103.05°103.05°

Bot · Answer

Let's call the angle 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)

Multiplying both sides by 8 gives:

720-8x = 180-x

Simplifying:

7x = 540

x = 77.14

So the supplement of x is 180-x = 102.86, which is answer choice A.