it really depends on the question. usually you would be given an angle in some way, and then they would tell you that it is supplementary to some other angle and then you would use the definition i said.
example. Given that A and B are supplementary angles. If A = 30 degrees, what is B?
here you would have A + B = 180 => 30 + B = 180 => B = 150 degrees
example. Given that A and B are supplementary angles measured in degrees, if A = 2x + 1 and B = x + 5, find x.
again you would set A + B = 180 => 2x + 1 + x + 5 = 180 and solve for x
the questions you get might not be that simple, but that's the gist of it. if angles are supplementary, you can equate their sum to 180 degrees or pi radians. similarly for complimentary angles, you can equate their sum to 90 degrees or pi/2 radians