The ratio of boys to girls on a class is 2to 3 there are 12 boys how many girls are there

Supplementary angles are adjacent angles which add to 180 degrees. Let's define the angles:

Let x and y define the two angles, and let's say x is the larger of the two angles
We can write two equations:
x+y = 180 (definition of supplementary angles)
x-y = 32  (given)

Add the equations together to eliminate y:

2x = 212 [divide both sides by 2]
x=106
The other angle is 180-106 = 74