One angle measures 58.6 degrees, and its supplementary angle would be 121.4 degrees.
To solve this problem, let's use algebra. Let's assume the measure of one angle is x degrees. The measure of its supplementary angle would then be 180 - x degrees. According to the problem, the given angle is 62.8 degrees less than its supplementary angle. So, we can write the equation:
x = (180 - x) - 62.8
Simplifying the equation, we have:
2x = 117.2
x = 58.6
Therefore, one angle measures 58.6 degrees, and its supplementary angle would be 180 - 58.6 = 121.4 degrees.