Question

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

​

Answer 1

Therefore the measures of the angles are 22.5° and 67.5°.

Explanation:

Complementary Angles:

Two angles are Complementary when they add up to 90 degrees.

Example 40° and 50° are Complementary Angles.

If 'x' and 'y' are Complementary Angles the we have

`x+y=90\°`

Here,

Let the common multiple be 'x '

Then the the Complementary Angles will be 'x' and '3x'.

`x+3x=90` ....property of Complementary Angles.

Solving the equation we get

`4x=90\\\\x=(90)/(4)=22.5`

Substituting 'x' values we get

x= 22.5°

3x = 3 × 22.5 = 67.5°

Therefore the measures of the angles are 22.5° and 67.5°.