SOLUTION: Find the measure of an angle such that twice the measure of its compliment is 16 more than the difference between the measures of its supplement and its compliment

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Question 466371: Find the measure of an angle such that twice the measure of its compliment is 16 more than the difference between the measures of its supplement and its compliment
Answer by Math-Help(7) About Me  (Show Source):
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Let x = original angle
The compliment of x: (90-x)
The supplement of x: (180-x)
Given:
2(90-x) = (180-x) - (90-x) + 16
****Now solve for x.
180-2x = (180-x) - (90-x) + 16...............Distribute 2 on lefthand side.
180-2x = 180 - x - 90 + x + 16...........Distribute "-" on righthand side.
180 - 180 + 90 - 16 = 2x - x + x......Combine like terms to opposite sides.
74 = 2x....................................Reduce like terms on both sides.
37 = x...............................Divide both sides by 2 to solve for x.
****Now check to see if it is correct.
2(90-37) =?= (180-37) - (90-37) + 16
2(53) =?= (143) - (53) + 16
106 =?= 90 + 16
106 = 106
Correct! It check's out!