Introduction:
Supplementary angles are a pair of angles that add up to 180 degrees. In this problem, we are given that two supplementary angles are in a ratio of 3:7. We need to find the difference between these angles.

Given:
Ratio of the angles: 3:7

Step-by-Step Solution:
1. Let's assume the measure of one angle as 3x, and the measure of the other angle as 7x, where x is a constant.
2. According to the given information, the sum of these two angles is 180 degrees because they are supplementary.
3. So, we can write the equation as: 3x + 7x = 180 degrees.
4. Combining like terms, we get: 10x = 180 degrees.
5. To find the value of x, we can divide both sides of the equation by 10: x = 18 degrees.
6. Now, we can find the measure of each angle by substituting the value of x back into the expressions:
- First angle: 3x = 3 * 18 = 54 degrees.
- Second angle: 7x = 7 * 18 = 126 degrees.
7. Finally, to find the difference between these angles, we subtract the smaller angle from the larger angle: 126 - 54 = 72 degrees.

Answer:
The difference between the two supplementary angles in the given ratio of 3:7 is 72 degrees.