SOLUTION: the measue of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle.

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Question 51577: the measue of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle.
Answer by rchill(405) About Me  (Show Source):
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Supplementary angles are those that add up to 180, and complementary angles add up to 90. Let x represent the angle; then (180-x) is the supplementary angle and (90-x) is the complementary angle. Three times the measure of the complement is represented by 3*(90-x) and 60 less than that produces 3%2A%2890-x%29-60. We're told that 3%2A%2890-x%29-60=180-x. So now we just solve algebraicly. Expanding the equation produces 270-3x-60=180-x. Now we combine like terms to get 210-3x=180-x. Now add 3x to both sides to get 210-3x%2B3x=180-x%2B3x, or 210=180%2B2x. Now subtract 180 from both sides 210-180=180%2B2x-180, or 30=2x. Dividing both sides by 2 30%2F2=2x%2F2 simplifies to 15=x. So, our angle is 15, its complement is 75, and its supplement is 165.