Question

The question that I'm having issues with is, "The complement of an angle, A, in degrees, is equal to one-sixth of the supplement of the angle, also in degrees.  Then A= "
I know the answer is 72 degrees, but I don't know how to figure the problem out!

Answer 1

$90-A=\frac{180-A}{6}\\ 540-6A=180-A\\ 5A=360\\ A=72$

Answer 2

'Complement' = difference between an angle an 90 degrees.

'Supplement' = difference between an angle and 180 degrees.

Complement of A = 90 - A

Supplement of A = 180 - A

The problem says that the complement is 1/6 of the supplement, right ?

So      90 - A = (1/6) x (180 - A)

Multiply each side of this equation by 6 :

540 - 6 A = 180 - A

Subtract 180 from each side:

360 - 6 A = - A

Add 6A to each side :

360 = 5 A

Divide each side by 5 :

A = 72°