Final answer:
The problem involves finding two supplementary angles where one is 22 degrees more than the other. By setting up an equation based on the property that supplementary angles sum up to 180 degrees, we determine the angles to be 79 degrees and 101 degrees respectively.
Step-by-step explanation:
To solve the problem where one angle measures 22 degrees more than its supplementary angle, let's use the fact that supplementary angles add up to 180 degrees.
Let's denote the smaller angle as x. Accordingly, the larger angle will be x + 22 degrees. Since they are supplementary, their sum is 180 degrees, so we have:
x + (x + 22°) = 180°
Simplifying this equation, we get:
2x + 22° = 180°
2x = 180° - 22°
2x = 158°
x = 79°
So the smaller angle measures 79 degrees, and the larger angle measures x + 22°, which is 79° + 22° = 101 degrees.