Final answer:
The first angle measures 45 degrees and its supplementary angle measures 135 degrees, as supplementary angles add up to 180 degrees.
Step-by-step explanation:
To solve this problem, let's designate the first angle as x degrees. Since angles are supplementary if they add up to 180 degrees, we can say that the measure of the supplementary angle to x is 180 - x degrees.
The problem states that the first angle is 90 degrees less than the measure of its supplementary angle, which means x = (180 - x) - 90. Simplifying this equation, we get x = 90 - x, which leads to 2x = 90.
Therefore, x = 45. This means the first angle measures 45 degrees, and its supplementary angle measures 135 degrees since 180 - 45 = 135.