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Question 504390: an angle measures 5 degrees more than 4 times its complement . find the measure of the angle.
pless i want help
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The complement of an angle is an angle that when added to the given angle results in an angle of 90 degrees.
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Therefore, let's call the angle that you are given angle A. The complement to angle A is 90 - A.
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You are told that angle A is 5 degrees more than 4 times its complement. Its complement is (90 - A) and 4 times its complement is therefore, 4(90 - A). You add 5 degrees to that product and the result is angle A. In equation form this is:
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A = 4(90 - A) + 5
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Do the distributed multiplication on the right side and you have:
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A = 360 - 4A + 5
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Collect the A terms on the left side by adding 4A to both sides:
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A + 4A = 360 - 4A + 4A + 5
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On the right side the -4A and +4A cancel each other out and on the left side the A + 4A adds to give 5A. So the equation becomes:
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5A = 360 + 5
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Total the right side:
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5A = 365
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Solve for A by dividing both sides by 5:
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A = 365/5
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The division on the right side gives:
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A = 73 degrees
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That should be the answer. Let's check it. If the angle is 73 degrees, its complement (the angle that must be added to make it 90 degrees) is 17 degrees (from 90 - 73). Multiply 4 times this complement (4 times 17) and you get 68 degrees. Then to that add 5 degrees and you get 73 degrees just as the problem says you should get. So the answer checks. The angle you were to find is 73 degrees.
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