First we need to define our conditions. Since the angles are complimentary, the sum of the angles must be equal to 90 degrees.
let x = first angle
y = second angle
x + y = 90
from the second condition in the problem
x + y =72 + x -y
solving for x
x= 54
therefore the shorter side is 90 - 54 = y
y = 36 degree, the shorter side
