Question

Two angles are complementary. The measure of one angle is 125% of the other. Find the measures of both angles.

Answer 1

To find the measures of two complementary angles where one is 125% of the other, set up an equation, solve for the smaller angle, and then calculate the larger angle. The measures of the complementary angles are 40 degrees and 50 degrees.

Step-by-step explanation:

When two angles are complementary, they add up to 90 degrees. If one angle is 125% of the other, we can describe the angles using algebra. Let's call the smaller angle x. Then the larger angle is 1.25x (or 125% of x). The equation to find the angles is x + 1.25x = 90 degrees.

Solving this equation:

1. Combine like terms: 2.25x = 90
2. Divide both sides by 2.25 to find x: x = 90 / 2.25
3. x equals 40 degrees
4. Now find 1.25x: 1.25x = 1.25 * 40 = 50 degrees

Therefore, the measures of the complementary angles are 40 degrees and 50 degrees.