Question 711078
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+S-C=180-90}}}
Simplify this. The A term goes away since A-A=0:
{{{S-C=90}}}
Solve for S:
{{{S=90+C}}}
Substitute this expression for S into Equation #1:
{{{C+90+C=190}}}
Solve for C:
{{{2C=100}}}
{{{C=50}}}
Now that you know C, you can substitute that into Equation #2 to find A:
{{{A+50=90}}}
{{{highlight(A=40)}}}
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Good Luck,
tutor_paul@yahoo.com