SOLUTION: What angle is a fifth of its complement

Click here to see ALL problems on Angles

Question 1142324: What angle is a fifth of its complement
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
15

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x be the angle.

let y be its complement.

x + y = 90 if the angles are complements of each other.

if the angle is 1/5 of its complement, then y = 5x.

replace y with 5x in the equation of x + y = 90 to get:

x + 5x = 90

combine like terms to get 6x = 90

solve for x to get x = 90/6 = 15 degrees.

the angle is 15 degrees.

its complement is 5 times as large, making it equal to 5 * 15 = 75 degrees.

the angle plus its complement is equal to 90 degrees because 15 + 75 = 90.

your solution is that the angle is 15 degrees.

15 / 75 = 1 / 5.

another way to solve this is as follows.

the angle is x.

the complement is 90 - x.

the angle is 1/5 its complement leads to x = 1/5 * (90 - x)

simplify to get x = 1/5 * 90 - 1/5 * x

simplify to get x = 18 - 1/5 * x

add 1/5 * x to both sides of the equation to get 6/5 * x = 18

multiply both sides of this equation by 5/6 to get x = 5/6 * 18

solve for x to get x = 15.

same answer solved in a different way.