The supplement of an angle is nines times as large as the complement of the angle. What is the measure of the angle to the nearest hundredth of a degree?

Answer 1

Let the angle be x degrees.
The supplement of the angle is 180 - x degrees.
The complement of the angle is 90 - x degrees.
According to the problem, we have the equation:
180 - x = 9(90 - x)

Solving for x, we get:
180 - x = 810 - 9x
8x = 630
x = 78.75

Therefore, the angle measures approximately 78.75 degrees to the nearest hundredth of a degree.