Let the measure of the angle be x degrees.
Since the angle is four times the measure of its supplementary angle, we can write:
x = 4(180 - x)
Expanding the right side, we get:
x = 720 - 4x
Adding 4x to both sides, we get:
5x = 720
Dividing both sides by 5, we get:
x = 144
So, the measure of the angle is 144 degrees, and the measure of its supplementary angle is 180 - 144 = 36 degrees.