SOLUTION: Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.

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Question 248897: Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
complement of an angle is 90 degrees minus the angle.

let a be the angle.

a = (90-a)/2 - 18

this means that the angle equals half its complement minus 18 degrees.

this means the same as the angle equals 18 degrees less than half its complement.

solve for a.

equation is:

a = (90-a)/2 - 18

simplify by removing parentheses to get:

a = 90/2 - a/2 - 18

simplify further to get:

a = 45 - a/2 - 18

combine like terms to get:

a = 27 - a/2

add a/2 to both sides to get:

a + a/2 = 27

multiply both sides of the equation by 2 to get:

2a + a = 54

combine like terms to get

3a = 54

divide both sides of the equation by 3 to get:

a = 18

your answer should be that the angle is equal to 18 degrees.

if the angle is 18 degrees, then its complement is equal to 90 - 18 = 72 degrees.

half its complement is equal to half of 72 is equal to 36 degrees

18 degrees less than that is equal to 36 - 18 is equal to 18 degrees.

Your answer is that the measure of the angle is 18 degrees.