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