The measures of two complementary angles are complementary angles are in the ratio 1:3. What are the measures of the angles?

The measure of angles are 22.5 degree and 67.5 degree

Solution:

Given that, measures of two complementary angles are in ratio 1 : 3

one angle : another angle = 1 : 3

Let the first complementary angle 1x

Let the another complementary angle be 3x

If the angles are complementary, then their sum is 90 degrees

Therefore,

1x + 3x = 90

4x = 90

x = 22.5

Then, first angle = 1x = 1 (22.5) = 22.5

Another angle = 3x = 3 (22.5) = 67.5

Thus the measure of angles are 22.5 degree and 67.5 degree