Let's denote the two supplementary angles as x and y.
According to the problem, the difference between these two angles is 54°. Mathematically, we can express this as:
x - y = 54.
Since the angles are supplementary, their sum is 180°. So, we can also write:
x + y = 180.
Now we have a system of two equations:
x - y = 54
x + y = 180.
To solve this system, we can use the method of elimination. Adding the two equations together eliminates the y term:
(x - y) + (x + y) = 54 + 180.
This simplifies to:
2x = 234.
Dividing both sides by 2, we get:
x = 117.
Substituting the value of x back into one of the equations, we can find y:
117 + y = 180.
Simplifying, we find:
y = 180 - 117,
y = 63.
Therefore, the two supplementary angles are 117° and 63°.