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
