SOLUTION: I am having a difficult time translating a word problem into an equation. The question is... Find the measure of an angle such that the difference between the measures of its su

Question 307555: I am having a difficult time translating a word problem into an equation. The question is...
Find the measure of an angle such that the difference between the measures of its supplement and three times its complement is 10 degrees.
I have tried
(x-180)-3(x-90)=10
and
3(x-90)-(x-180)=10
I know that the answer is 50 because it is in the back of the book. Neither one of my equations worked out to be 50, so I know that I must be reading the word problem wrong. I can't figure this out, please help!!!
Found 3 solutions by rapaljer, Earlsdon, nerdybill:
Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!
If x is the angle, then 90-x is the complement and 180-x is the supplement. You used x-90 and x-180. If you fix this, I think the first equation you wrote is correct.

Dr. Robert J. Rapalje, Retired
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Let the angle be A, then its complement is (90-A) and its supplement is (180-A).
(You have these two backwards!), so...
(180-A)-3(90-A) = 10 Simplify.
180-A-270+3A = 10 Combine the A's and the numbers.
(180-270)+(-A+3A) = 10
-90+2A = 10 Add 90 to both sides.
2A = 100 Divide both sides by 2.
A = 50 degrees.

Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Find the measure of an angle such that the difference between the measures of its supplement and three times its complement is 10 degrees.
.
Let x = angle
then
complement is 90-x
supplement is 180-x
.
From:"the difference between the measures of its supplement and three times its complement is 10 degrees"
(180-x) - 3(90-x) = 10
180-x - 270+3x = 10
180 - 270+2x = 10
-90+2x = 10
2x = 100
x = 50 degs

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