**What is Complementary Angles?**

Two Angles are said to be Complementary Angles, if the sum of their measure is 90˚.

### Complementary Angles Examples:

- In this figure, two angles i.e, 55˚ and 35˚ are Complementary Angles.

As, 55˚ + 35˚ = 90˚

- In this figure, two angles i.e, 60˚ and 30˚ are Complementary Angles.

As, 60˚ + 30˚ = 90˚

**Example 1**

If one of the two Complementary Angles is 24˚ , what is the measure of the other Angle ?

**Explanation**

Two Angles are said to be Complementary Angles, if the sum of their measure is 90˚.

Measure of one Angle = 24 ˚

Let the Measure of the Second Angle be =x ˚

Sum of Complementary Angles =90 ˚

In other words, 24˚ + x˚ = 90˚

x˚ = 90˚ – 24˚

x˚ = 66˚

Hence, the measure of the other Angle is = 66˚

**Example 2**

The difference in the measure of two Complementary Angles is 6˚ . Find the measure of Angles?

**Explanation**

Two Angles are said to be Complementary Angles, if the sum of their measure is 90˚.

Let the measure of one Complementary Angle = ( x )˚

Then, the measure of other Angle = ( x – 6 )˚

Sum of Complementary Angles = 90˚

x˚ + x˚ – 6˚ = 90˚

2x˚ = 90˚ + 6˚

2x˚ = 96˚

x =

x = 48

Hence, the measure of one Angle = ( x )˚ = 48˚

The measure of other Angle = ( x – 6 )˚ = ( 48 – 6)˚ = 42˚

**Example 3**

If two Complementary Angles are in the ratio 1 : 4 , find the measure of Angles?

**Explanation**

Two Angles are said to be Complementary Angles, if the sum of their measure is 90˚.

Let the measures of two Angles be ( 1a )˚ and ( 4a )˚

Sum of Complementary Angles = 90˚

( 1a )˚ + (4a )˚ = 90˚

( 5a )˚ = 90˚

a =

a = 18

Hence, measure of two Angles are:

( 1a )˚ = ( 1 x 18 )˚ = 18˚

( 4a )˚ = ( 4 x 18 )˚ = 72˚

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