Answer:
58.5° and 31.5°
Explanation:
Complementary angles are two angles whose sum is 90 degrees. Let x be one of the complementary angles, then the other complementary angle can be represented as 90 - x.
The problem tells us that the difference between the two complementary angles is 27 degrees, so we can set up the following equation:
x - (90 - x) = 27
Simplifying and solving for x, we get:
x - 90 + x = 27
2x - 90 = 27
2x = 117
x = 58.5
So one of the complementary angles is 58.5 degrees, and the other complementary angle can be found by subtracting this value from 90:
90 - 58.5 = 31.5
Therefore, the measures of the angles are [58.5° and 31.5°.]