SOLUTION: Half the supplement of an angle is 12 degrees less than twice the complement of the angle. Find the measure of the angle.

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Question 200873: Half the supplement of an angle is 12 degrees less than twice the complement of the angle. Find the measure of the angle.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Half the supplement of an angle is 12 degrees less than twice the complement of the angle.
Find the measure of the angle.
:
Let the angle be x:
:
Write a equation for the statement:
"Half the supplement of an angle is 12 degrees less than twice the complement of the angle."
1%2F2(180-x) = 2(90-x) - 12
Multiply both sides by 2 to get rid of the fraction, results:
180 - x = 4(90-x) - 24
:
180 - x = 360 - 4x - 24
-x + 4x = 360 - 24 - 180
3x = 156
x = 156%2F3
x = 52 degrees is the angle
;
:
Check solution in the original equation:
1%2F2(180-52) = 2(90-52) - 12
1%2F2(128) = 2(38) - 12
64 = 76 - 12