Posted by Shane on .
I have tried this problem a few ways, and I am getting frustrating results. Could you help me out by showing me how to set the systems of equations
Two angles are complementary The sum of the measure of the first angle and 1/4 the second angle is 82.5. Find the measure of the angles.
I think that the first equation will look like this: x+y=82.5, but I am stuck on the set up of the second one.

Math 
MathMate,
The first step in setting up equations
is to define the unknowns. Then reread the question and interpret the data as equations in terms of the defined unknowns. Finally, solve the mathematical equation(s).
Let x=first anlge, y=second angle
"Two angles are complementary":
x+y=90 ..... (1)
"The sum of the measure of the first angle and 1/4 the second angle is 82.5"
x + y/4 = 82.5 .....(2)
In general, I would be tempted to minimize the number of variables if there is a simple relationship between two variables. You could also do:
From x+y=90, write y=90x
instead of writing
x+y/4=82.5
write
x+(90x)/4 = 82.5 .....(3)
Solve for x in (3), one unknown and one equation.