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Question 308893: The measure of the supplement of an angle is six times the measure of it's complement. Find the measures of the angle, its supplement, and its complement
Answer by mollukutti(30)   (Show Source):
You can put this solution on YOUR website! Basic facts:
1. Complementary angles add upto 90 degrees
2. Supplementary angles add upto 180 degrees
Let us consider the angle as x degrees
Therefore its complementary angle will be (90 - x) degrees
Also its supplementary angle will be (180 - x) degrees
As per the question the supplement of the angle is 6 times its complement angle.
Therefore we can write the equation as:
180 - x = 6 x (90 - x)
or, 180 - x = 540 - 6x
or, 180 - x + 6x = 540 (Bring the variables to left side)
or, -x + 6x = 540 - 180 (bring the numbers to the right side)
or, 5x = 360
or 5x/5 = 360/5 (divide both sides by 5)
or, x = 72
Therefor the angle is 72 degrees
Complement = 90 - 72 = 18 degrees
Supplement = 180 - 72 = 108 degrees
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