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Question 498619: When one-half the supplement of an angle is added to the complement of the angle, the sum is 120. What is the measure of the complement?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's call the unknown angle A. Then its supplement is 180-A and its complement is 90-A.
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Therefore, 1/2 of the supplement of angle A can be written as (1/2)*(180-A). It gets added to the complement as follows:
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(1/2)*(180-A)+ (90-A)
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and this is to equal 120. So we can write the equation as:
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(1/2)*(180-A)+ (90-A) = 120
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Get rid of the 1/2 by multiplying all terms on both sides by 2 to get:
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180-A + 2(90-A) = 240
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Do the distributed multiplication on the left side:
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180 - A + 180 - 2A = 240
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add 180 + 180 on the left side:
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360 - A - 2A = 240
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combine the A terms:
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360 - 3A = 240
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Subtract 360 from both sides:
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-3A = -120
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Multiply both sides by -1:
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3A = 120
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Solve for the unknown angle by dividing both sides by 3 to get:
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A = 120/3 = 40
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So the unknown angle is 40 degrees. That means that its complement is 90 - 40 = 50 degrees.
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This also means that its supplement is 180 - 40 = 140 degrees. Therefore, a half of its supplement is 70 degrees and when added to the 50 degree complement the total is 120 degrees, just as the problem said it should be. Everything checks.
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In summary, the complement that you were to find is 50 degrees.
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Hope this helps you to understand the problem a little better.
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