Final answer:
To solve for two complementary angles where one is 1/5 of the other, set up the equation (6/5)x = 90, where x represents the larger angle. Solve to find that the larger angle is 75 degrees, and the smaller angle is 15 degrees.
Step-by-step explanation:
To find the measures of two complementary angles, where one angle is 1/5 of the other, start by setting up an equation based on the fact that complementary angles add up to 90 degrees.
Let x represent the measure of the larger angle, and (1/5)x represent the measure of the smaller angle.
The equation would then be x + (1/5)x = 90. Solving for x, we get that (6/5)x = 90, which means that x = (5/6) * 90. Therefore, x = 75 degrees for the larger angle, and the smaller angle is 1/5 of that, so (1/5) * 75 = 15 degrees.