Find the degree measure on an angle whose complement twelve twenty-sevenths of its supplement. Determine the angle's complement?
Let the angle be x °.
If the complement is 12/27 of its supplement, then
x = (12/27)(180-x)
solve for x.
Calculate 90-x as its complement.
2.25
To find the degree measure of an angle, we need to first understand what the terms "complement" and "supplement" mean.
Complementary angles are two angles that add up to 90 degrees. So if the given angle is A, its complement would be 90 - A.
Supplementary angles, on the other hand, are two angles that add up to 180 degrees. Therefore, if the given angle is A, its supplement would be 180 - A.
Now, let's interpret the given information: "The complement of the angle is twelve twenty-sevenths of its supplement."
Mathematically, we can express this as:
Complement of the angle = (12/27) * Supplement of the angle
Using the equations we derived earlier, we can substitute in the appropriate values:
90 - A = (12/27) * (180 - A)
To solve this equation, we can simplify it by multiplying both sides by 27 to eliminate the fraction:
27(90 - A) = 12(180 - A)
Now, distribute the values:
2430 - 27A = 2160 - 12A
Combine like terms:
2430 - 2160 = 27A - 12A
270 = 15A
Now, divide both sides by 15 to solve for A:
A = 270 / 15
Simplifying gives:
A = 18
So, the measure of the angle is 18 degrees.
To determine the angle's complement, substitute this value of A into the complement equation:
Complement of A = 90 - A
Complement of A = 90 - 18
Complement of A = 72
Therefore, the angle's complement is 72 degrees.