The supplement of an angle measures 11 times its complement. Then the measure of the angle is...
A. 9 degrees
B. 81 degrees
C. 90 degrees
D. 99 degrees
E. 100 degrees
let the angle be x
then it's complement = 90-x
and it's supplement is 180-x
180-x = 11(90-x)
180-x = 990 - 11x
10x = 810
x = 81
To solve this problem, we need to first understand the definitions of the supplement and the complement of an angle.
The supplement of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. Mathematically, if the given angle measures x degrees, then its supplement would measure (180 - x) degrees.
The complement of an angle is the angle that, when added to the given angle, results in a sum of 90 degrees. Mathematically, if the given angle measures x degrees, then its complement would measure (90 - x) degrees.
Now, let's solve the problem step-by-step:
Given that the supplement of an angle measures 11 times its complement, we can write this as an equation:
Supplement = 11 * Complement
Let's denote the angle as "x" degrees. Therefore, the supplement of the angle is (180 - x) degrees, and the complement of the angle is (90 - x) degrees.
We can now rewrite the equation as:
(180 - x) = 11 * (90 - x)
Now, we simplify and solve for x:
180 - x = 990 - 11x
Adding 11x to both sides:
11x - x = 990 - 180
Simplifying:
10x = 810
Dividing both sides by 10:
x = 81
Therefore, the measure of the angle is 81 degrees.
So, the correct answer is option B. 81 degrees.