Let x be the measure of the angle and y be the measure of its supplementary angle.
Since the angle measures 72° less than its supplementary angle, we have the equation:
x = y - 72
And since the angles are supplementary, we also have:
x + y = 180
Substitute x = y - 72 into the second equation:
y - 72 + y = 180
2y - 72 = 180
2y = 252
y = 126
Now, substitute y = 126 back into x = y - 72:
x = 126 - 72
x = 54
Therefore, the angle measures 54° and its supplementary angle measures 126°.