SOLUTION: The measure of the supplement of an angle exceeds 4 times the measure of the complement by 24. Find the supplement.

Question 1167847: The measure of the supplement of an angle exceeds 4 times the measure of the complement by 24. Find the supplement.
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
angle is x
supplement is 180-x
complement is 90-x
so (90-x)*4+24=180-x
360-4x+24=180-x
3x=204
x=68 degrees, the angle.
the supplement is 112 degrees, the answer
the complement of the angle is 22 degrees.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the supplement of an angle is 180 minus the angle.

the complement of an angle is 90 minus the angle.

you are given that the supplement of the angle exceeds 4 times the complement of the angle by 24.

let x represent the angle.

you get:

180 - x = 4 * (90 - x) + 24

simplify to get:

180 - x = 360 - 4x + 24

subtract 180 from both sides of the equation and add 4x to both sides of the equation to get:

-x + 4x = 360 + 24 - 180

combine like terms to get:

3x = 204

solve for x to get:

x = 204/3 = 68.

the measure of the angle is 68 degrees.
the supplement of the angle is 180 - 68 = 112 degrees
the complement of the angle is 90 - 68 = 22 degrees.

the supplement of the angle is 112 degrees.
4 times the complement of the angle + 24 degrees = 4*22 + 24 = 112 degrees.

this confirms the solution is correct.

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