Final answer:
The measure of one angle is 56 degrees, and the measure of the other angle is 34 degrees.
Step-by-step explanation:
To find the measures of the angles, we need to use the fact that the angles are complementary. Complementary angles add up to 90 degrees. Let's call one angle x, and the other angle will be 90 - x since their sum is 90 degrees. Given that the difference in their measures is 22 degrees, we can set up the equation x - (90 - x) = 22. Solving this equation will give us the value of x, and we can then find the measure of the other angle.
Simplifying the equation, we have x - 90 + x = 22. Combining like terms, we get 2x - 90 = 22. Adding 90 to both sides, we have 2x = 112. Dividing both sides by 2, we get x = 56. So one angle is 56 degrees, and the other angle is 90 - 56 = 34 degrees.
Learn more about Complementary angles