The supplement and the angle in this problem must add to 180 degrees.
Since the ratio is 3:5, this means that there is a common multiplier (in this case angle) that when compared between the angle and the supplement of the angle give the ratio of 3:5.
Since that common factor or multiplier can be treated as X, we can set up an expression as 3x + 5x = 180.
This will give you an incremental angle, X. If you then multiply by 3 you obtain the angle and multiplying X by 5 will give you its supplement angle.
Another way to look at it is once you obtain your angle from 3*x, then you could also subtract it from 180 to obtain the supplement.