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 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.
To find the measure of the angle, let's first understand the definitions of complement and supplement of an angle.
The complement of an angle is the angle that, when added to the given angle, equals 90 degrees.
The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees.
Let's assume the measure of the angle is "x" degrees.
According to the problem, the supplement of the angle (180 - x) is nine times as large as the complement of the angle (90 - x). We can write this as an equation:
180 - x = 9(90 - x)
Let's solve this equation step by step:
180 - x = 810 - 9x (Distribute 9 to both terms inside the parentheses)
-x + 9x = 810 - 180 (Simplify the left side, combining like terms)
8x = 630
x = 630/8
x ≈ 78.75
Therefore, the measure of the given angle is approximately 78.75 degrees to the nearest hundredth.
Let's assume the measure of the angle is x degrees.
The complement of the angle is 90 - x degrees.
The supplement of the angle is 180 - x degrees.
According to the given information, the supplement of the angle is nine times as large as the complement of the angle:
180 - x = 9(90 - x)
Simplifying the equation:
180 - x = 810 - 9x
Combining like terms:
8x = 630
Dividing both sides by 8:
x = 78.75
Therefore, the measure of the angle is approximately 78.75 degrees.