Question

Find the measures of the complementary angles that satisfy each case. One of the angles is 3 times larger than the other.

Answer 1

22.5° and 67.5°

Explanation:

The sum of complementary angles equal 90°.

Given that one of the complementary angles is 3 times larger than the other, let "x" represent the other angle.

Thus, the following expression can be written to represent this case:

`x + 3x = 90`

Solve for x

`4x = 90`

Divide both sides by 4

`(4x)/(4) = (90)/(4)`

`x = 22.5`

The measure of the complementary angles are:

x = 22.5°

3x = 3(22.5) = 67.5°