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Question 476525: Q: Find the measure of two supplementary angles if one angle is 20 degrees more than four times the other.
this is what I think it is, but not sure!
4x+20=180
4x=140
x=35
angle 1= 35
angle 2= 35
angle 3= 110
is this correct?
thanks!!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The problem says there are two supplementary angles. You are looking for two angles, not three. By the definition of supplementary angles, you are looking for two angles whose whose measures when added result in a total measure of 180 degrees.
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Let's call the measure of one angle x.
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The measure of the other angle is 4 times the other plus 20 degrees. In algebraic terms this is 4x + 20.
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When you add the measures of these two angles, the total is to be 180 degrees. In equation form this is:
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x + (4x + 20) = 180
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Combine the terms containing x and the equation becomes:
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5x + 20 = 180
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Get rid of the 20 on the left side by subtracting 20 from both sides:
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5x = 160
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Solve for x by dividing both sides by 5:
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x = 180/5 = 32
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So one of the angles is 32 degrees. The other angle must therefore be 180 - 32 = 148 degrees.
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You can also check to see what 4 times 32 + 20 equals. 4 times 32 = 128 degrees and then add 20 more degrees and you have 148. So that checks.
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The measures of the two supplementary angles that satisfy this problem are 32 and 148 degrees.
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Hope this helps you understand the problem a little better.
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