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?
Let's start by defining the terms "supplement" and "complement" of an angle.
The supplement of an angle is the angle that, when added to the original angle, equals 180 degrees.
The complement of an angle is the angle that, when added to the original angle, equals 90 degrees.
Let x be the measure of the angle in degrees.
According to the problem, we know that:
180 - x = 9(90 - x)
Simplifying this equation:
180 - x = 810 - 9x
8x = 630
x = 78.75
Therefore, the measure of the angle to the nearest hundredth of a degree is 78.75 degrees.