Question

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

Answer:

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

Step-by-step 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

$4x=90\\\\x=\dfrac{90}{4}=22.5$

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°.