SOLUTION: The sum of the complement and the supplement of an angle is 190. What is the measure of the angle?

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Question 711078: The sum of the complement and the supplement of an angle is 190. What is the measure of the angle?
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Define the following variables:
A=Angle you are looking for
C=A's Complement
S=A's Supplement
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You can write the following equations:
Equation 1: C+S=190
Equation 2: A+C=90
Equation 3: A+S=180
You have 3 equations and 3 unknowns. Anytime you can write as many equations as you have unknowns, you can solve the problem.
There are several ways to proceed from here. Here is one way:
Subtract Equation #2 from Equation #3:
A-A%2BS-C=180-90
Simplify this. The A term goes away since A-A=0:
S-C=90
Solve for S:
S=90%2BC
Substitute this expression for S into Equation #1:
C%2B90%2BC=190
Solve for C:
2C=100
C=50
Now that you know C, you can substitute that into Equation #2 to find A:
A%2B50=90
highlight%28A=40%29
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Good Luck,
tutor_paul@yahoo.com