Question

How do you find the measure of an angle if it’s six times the supplementary angle?

Answer 1

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