SOLUTION: Dear sir/madam, Thank you or taking the time to help me solve my problem. Here it is: Problem: If the complement of an angle is 5� less than one-sixth of its supplement, f

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Question 935139: Dear sir/madam,
Thank you or taking the time to help me solve my problem. Here it is:
Problem:
If the complement of an angle is 5� less than one-sixth of its supplement, find the measure of the angle.
My attempt: (I'm having trouble writing the equation!!!)
Complimentary angles = 90 degrees, therefore:
90 - a
Supplementary angles = 180 degrees therefore:
180 - 1/6a - 5
Therefore:
90 -a = 180 -1/6a - 5
6(90) - 6(a) = 6(180) - 6(1/6)a - 6(5)
540 - 6a = 1080 - a - 30
540 - 6a = 1050 - a
540 - 540 - 6a = 1050 - 540 - a
- 6a = 510 - a

- 6a + a = 510
- 5a = 510
- 5a/5 = 510/5
-a = 102
a = - 102
Obviously an angle can't be negative so I must have written the wrong equation.
Any help you could provide would be most appreciated.
Kindest regards,
Mark Beaton
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
If the complement of an angle is 5� less than one-sixth of its supplement, find the measure of the angle.

;et angle be x
complimentary angle = (90-x)
supplementary angle = (180-x)
0n-sixth = (180-x)/6
5 less than = (180-x)/6 - 5
(90-x) =((180-x)/6) -5
90+5 = (180-x)/6 +x
95 = (180-x+6x)/6
570 = 180+5x
390 = 5x
x= 78 deg

Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
x, the angle's measure.
90-x, the complement.
180-x, the supplement.

If the is PLUS , find the measure of the angle, x.

Form this equation:

Solve the equation for x.