SOLUTION: The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement of the angle?

Question 1139371: The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement of the angle?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = the angle.
90 - x = the supplement of the angle.
180 - x = the supplement of the angle.

the complement of the angle is 1/6 the measure of the supplement of the angle.

the equation for this is (90 - x) = 1/6 * (180 - x).

simplify to get 90 - x = 1/6 * 180 - 1/6 * x.

simplify further to get 90 - x = 30 - 1/6 * x.

subtract 30 from both sides of the equation and add x to both sides of the equation to get 90 - 30 = x - 1/6 * x.

simplify to get 60 = 5/6 * x.

solve for x to get 6/5 * 60 = x.

this results in x = 72 degrees.

the complement of 72 degrees is 90 - 72 = 18 degrees.

the supplement of 72 degrees is 180 - 72 = 108 degrees.

18 * 6 = 108 degrees, so the complement of the angle is equal to 1/6 * the supplement of the angle.

not sure what they're looking for.

if it's the angle, then the solution is 72 degrees.
if it's the complement of the angle, then the solution is 18 degrees.
if it's the supplement of the angle, then the solution is 108 degrees.

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