SOLUTION: The measure of a supplement of an angle is 12 degrees greater then 3 times the measure of a complement. Find the measure of the angle.

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Question 155475: The measure of a supplement of an angle is 12 degrees greater then 3 times the measure of a complement. Find the measure of the angle.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Let's bisect the problem carefully.
First illustration:
A and B are supplementary angles, so A%2BB=180 -----> eqn 1
It shows B is a supplement of A and a highlight%28condition%29 exist that the supplement which is B, is 12 degrees greater than 3 times the complement.
2nd illustration:
We make again A and B complementary angles this time, so
A%2BB=90 ----> eqn 2. we make A a complement of B. To show the condition on the 1st illustration: highlight%28B=12%2B%283A%29%29----> 12 greater than 3 times the complement, being A a complement of B right?
Substitute the highlight%28condition%29 to eqn 1:
A%2B12%2B3A=180
4A=180-12=168
cross%284%29A%2Fcross%284%29=cross%28168%2942%2Fcross%284%29
A=42degrees
For B in question via eqn 1:42%2BB=180
B=180-42=138degrees
To check, go back to the highlight%28condition%29:
B=12%2B%283A%29
138=12%2B%283%2A42%29
138=12%2B126
138deg=138deg
Thank you,
Jojo