Question

Two complementary angles have measures in the ratio of 1 to 5. Find the measure of each angle.

15 and 75
18 and 72
30 and 150
36 and 144

Answer 1

15 and 75. I had this same question on a test.

Answer 2

15° and 75°

Explanation:

We are given that the two complementary angles have the measures in ratio 1 : 5.

Let the measure of one angle be x°.

Since, the ratio is 1 : 5.

This gives us that the angle measure of other angle will be 5x°.

Now, we know that the sum of complementary angles is 90°.

So, x° + 5x° = 90°

i.e. 6x° = 90°

i.e. x =
`(90)/(6)`

i.e. x = 15°

This gives that 5x° = 5 × 15° = 75°.

Hence, the angle measures are given by 15° and 75°.