SOLUTION: My son and I have been working on this for hours twice the supplement of the complement of an angle is 60 degrees more than the supplement of the angle. find the complement of the

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Question 104853: My son and I have been working on this for hours
twice the supplement of the complement of an angle is 60 degrees more than the supplement of the angle. find the complement of the angle
Found 2 solutions by edjones, Earlsdon:
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
let the angle be x
complement=90-x
supplement=180-x
supplement of the complement=(180-(90-x))
So, 2(180-(90-x))=60+180-x
2(180-90+x)=240-x
360-180+2x=240-x
3x=240-360+180
3x=60
x=20 degrees
Check:
compliment (20)=70
suppliment (20)=160
suppliment of compliment (70)=110
2*110=60+160
220=220
.
Ed

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
First, let's find the angle, which we can call angle A, then we can find its complement (90-A) to answer the problem.
The supplement of A is 180-A and the complement of A is 90-A
From the problem description, we can write:
2(180-(90-A)) = (180-A)+60 Simplify this and solve for A
2(180-90+A) = 180+60-A
2(90+A) = 240-A
180+2A = 240-A Add A to both sides of the equation.
180+3A = 240 Now subtract 240 from both sides.
3A = 60 Finally, divide both sides by 3.
A = 20 degrees. Now we can find the complement of A (90-A) as required by the problem.
90-A = 90-20 = 70 degrees.
The solution is:
The complement of the angle is 70 degrees.