SOLUTION: Please help me solve this problem: The supplement of an angle is 12 more than twice its compliment. Find the supplement of the complement of the angle.

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Question 913016: Please help me solve this problem:
The supplement of an angle is 12 more than twice its compliment. Find the supplement of the complement of the angle.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Complementary angles are angles that add up to 90 degrees.
Supplementary angles are angles that add up to 180 degrees.
let's angles be alpha and beta
alpha+%2B+beta=90 => alpha=90-beta and alpha is a complement of beta
alpha+%2B+beta=180 => alpha=180-beta and alpha is a supplement of beta
given: the supplement of an angle is 12 more than twice its compliment
180-beta=2%2890-beta%29%2B12 ...solve for beta
180-beta=180-2beta%2B12
2beta-beta=180-180%2B12
beta=12
then, alpha=180-beta =>alpha=180-12 =>alpha=168 -the supplement of angle beta
alpha=90-beta=> alpha=90-12=> alpha=78 ............complement of angle beta