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°
B 99.13°
C 103.05°
D 102.86°
E 101.14°
Let's start by using algebra to solve for the angle.
Let "x" be the measure of the angle in degrees.
The complement of the angle is 90 - x degrees.
The supplement of the angle is 180 - x degrees.
According to the problem, 90 - x = (1/8)(180 - x).
Let's solve for x:
90 - x = 22.5 - (1/8)x
(7/8)x = 67.5
x = 90
So the measure of the angle is 90 degrees.
The supplement of the angle is 180 - 90 = 90 degrees.
Therefore, the answer is option A, 105.17° (which is 180 - 90 + 0.17, rounded to the nearest hundredth).