SOLUTION: Find the measure of an angle, if six times its complement is 12° less than it's supplement

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Question 1084672: Find the measure of an angle, if six times its complement is 12° less than it's supplement
Found 2 solutions by MathLover1, Fombitz:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Two angles are complementary when they add up to 90 degrees.
Two angles are supplementary when they add up to 180 degrees.
alpha%2Bbeta=90........1)-> complement of alpha is 90-alpha
alpha%2Bbeta=180........2)->supplement of alpha is 180-alpha
if six times its complement is 12° less than it's supplement , we have
6%2890-alpha%29%2B12=180-alpha
540-6alpha%2B12=180-alpha
540-180%2B12=6alpha-alpha
372=5alpha
372%2F5=alpha
highlight%28alpha=74.4%29->the measure of your angle
then
-> complement of 74.4 is 90-74.4=15.6
->supplement of 74.4 is 180-74.4=105.6
check:
6%2890-alpha%29%2B12=180-alpha
6%2815.6%29%2B12=105.6
93.6%2B12=105.6
105.6=105.6


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A%2BS=180
A%2BC=90
So then subtracting,
A%2BS-A-C=180-90
S-C=90
and
6C=S-12
or
S=6C%2B12
Substituting,
6C%2B12-C=90
5C=78
Solve for C, then use either equation to solve for S.