Question 101410
If you are given the measure of an angle 1, then what is the measure of the angle of its 
supplement?
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Since the supplement of an angle is the angle that must be added to make the total 180 degrees.
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So the supplement of angle 1 (call it angle S) can be found by subtracting 
the measure 
of angle 1 from 180 degrees. In equation form this could be:
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mS = 180 - m1  [call this equation 1]
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or in words, the measure of the supplementary angle S equals 180 degrees minus the measure of
the angle 1.
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Next you are told that the measure of angle 1 equals 4 times the measure of angle S.
In equation form this is:
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m1 = 4*(mS) [call this equation 2]
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But from equation 1 we know mS = 180 - m1 . Therefore for mS we can substitute 180 - m1 
into equation 2 to get:
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m1 = 4*(180 - m1)
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Multiply out the right side. 4 times 180 = 720 and 4 times m1 = 4*m1. This makes the
equation become:
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m1 = 720 - 4*m1)
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You can get rid of the 4*m1 on the right side by adding 4*m1 to both sides to get:
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5*m1 = 720
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Solve for m1 by dividing both sides by 5 to get:
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m1 = 720/5 = 144 degrees.
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Since m1 = 144 degrees, its supplement is the angle that you add to 144 to get 180 degrees.
Therefore the supplement is 180 degrees minus 144 degrees which is 36 degrees.
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Check by finding out if the m1 equals 4 times its supplement. In other words, does 
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144 degrees = 4 times 36 degrees
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Multiply out the right side and it becomes 144 degrees, so our answer checks.
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Hope this helps you to understand the problem and figure out what you are doing.
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