SOLUTION: The difference between the supplement of an angle and twice its complement is 40. find the angle. its complement and supplement.

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Question 622257: The difference between the supplement of an angle and twice its complement is 40. find the angle. its complement and supplement.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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We want to find the measures of the angle, its complement and its supplement.
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Let a be the measure of the angle we are trying to find.
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The complement of a is 90-a because the sum of the measures of an angle and its complement is 90 degrees; notice that a + (90-a) = 90.
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The supplement of a is 180-a because the sum of an angle and its supplement is 180 degrees; notice that a + (180-a) = 180.
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In algebra, the phrase "twice its complement" can be written as 2*(90-a) or 180-2a. Since the difference between the supplement and twice the complement is 40, we write
%28180-a%29-%28180-2a%29=40
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Now simplify and solve for a.
180-a-180%2B2a=40
a=40
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In the context of this problem, the equation a=40 means that the measure of the angle is 40 degrees.
The complement of a has a measure of 50 degrees since 40+50=90. By similar reasoning, the supplement of a has a measure of 140 degrees.
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As a last step, we check our work against the original problem. We have "the difference between the supplement and twice the complement is 40. Twice 50 degrees is 100 degrees. The difference between 140 degrees and 100 degrees is 40 degrees. Check!
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Hope this helps. You are welcome to email me if any part does not make sense yet.
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Ms.Figgy
math.in.the.vortex@gmail.com