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

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

Answer 1

Let's call the measure of the angle in question "x."

The complement of x is 90 degrees minus x.
The supplement of x is 180 degrees minus x.

According to the problem, the complement of x is one-eighth the measure of the supplement of x:

90 - x = (1/8)(180 - x)

Simplifying this equation:

720 - 8x = 180 - x
540 = 7x
x = 77.14

So the measure of the angle x is 77.14 degrees.

To find the supplement of x, we subtract x from 180:

180 - 77.14 = 102.86

Therefore, the answer is (B) 102.86 degrees.