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