Supplementary angles are two angles which add up to 180 degrees. Complementary angles add up to 90 degrees.
Let's call our angle X, our supplement S, and our complement C. Based on the definitions, X + C = 90, and X + S = 180. We also know that 6C = S.
Combining the last two equations, we can say that X + 6C = 180, because S and 6C are the same. Subtracting 6C from both sides gives us X = 180 - 6C.
Now, combining our first equation with the one we just created, we can say that 180 - 6C + C = 90. This leads to:
180 - 5C = 90 (simplify)
180 = 90 + 5C (add 5C to both sides)
90 = 5C (subtract 90 from both sides)
18 = C (divide both sides by 5)
Now we know what our complement is. So, using X + C = 90:
X + 18 = 90
X = 72
Also:
6(18) = S
108 = S
So the angle is 72 degrees, the complement is 18 degrees, and the supplement is 108 degrees.
