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Question 495854: The measure of the complement of an angle times seven is equivalent to three times the supplement. Find the complement.
Attempt at solving:
90-7x = 3x
90 = 10x
9 = x
90-63 = 27
The complement is 27 degrees?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's work with the angle itself. Let x be the unknown angle.
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If x is the unknown angle, then its complement is 90 - x and its supplement is 180 - x.
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The problem then tells you that 7 times the complement equals 3 times the supplement. In equation form this is:
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7*(90 - x) = 3*(180 - x)
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Multiply out the two sides:
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630 - 7x = 540 - 3x
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Subtract 540 from both sides:
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90 - 7x = - 3x
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Add 7x to both sides:
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90 = 4x
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Solve for the unknown angle by dividing both sides by 4 to get:
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22.5 = x
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So the unknown angle is 22.5 degrees. Then its complement is 90 - 22.5 and that is 67.5 degrees.
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Its supplement is 180 - 22.5 and it equals 157.5 degrees.
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To check our answers, let's return to the original problem which states that 7 times the complement equals 3 times the supplement. In equation form this is:
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7*67.5 = 3*157.5
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and doing the multiplications shown on both sides results in:
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472.5 = 472.5
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Since both sides are equal, we know that the answer is correct. The complement that you were to find is 67.5 degrees.
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Hope this helps you to understand this problem a little better. This problem is made difficult by how it's written. Once you get the wording correctly interpreted into equation form, getting the solution is actually the easier part.
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