#### What is Supplementary Angles?

Two angles are said to be supplementary if the sum of their measure is 180^{o}

#### Supplementary Angles Examples

- In this figure, two angles i.e, 65˚ and 125˚ are Supplementary Angles.

As, 65˚ + 125˚ = 180˚

- In this figure, two angles i.e, 70˚ and 110˚ are Supplementary Angles.

As, 70˚ + 110˚ = 180˚

## Questions Based on Supplementary Angles

**QUESTION 1**

If two Angles are Supplementary, and one of the Angles is 65˚ , what is the measure of the other Angle?

**EXPLANATION**

If two Angles are Supplementary, then their sum of measures is 180˚

Measure of one Angle = 65˚

Let the Measure of the Second Angle be = x˚

Sum of Supplementary Angles = 180˚

In other words, 65˚ + x˚ = 180˚

x˚ = 180˚ – 65˚

x˚ = 115˚

Hence, the measure of the other Angle is = 115˚

**QUESTION 2**

The difference of the measure of two supplementary Angles is 10˚ . Find the measure of Angles.

**EXPLANATION**

If two Angles are supplementary, then their sum of measure is 180˚

Let the measure of one Angle = ( x )˚

Then, the measure of other Angle = ( x – 10 )˚

Sum of Supplementary Angles = 180˚

x˚ + x˚ – 10˚ = 180˚

2x˚ = 180˚ + 10˚

2x˚ = 190˚

x =

x = 95

Hence, the measure of one Angle = ( x )˚ = 95˚

and other Angle = ( x – 10 )˚ = ( 95 – 10)˚ = 85˚

**QUESTION 3**

Two supplementary Angles are in the ratio of 1 : 4 , find the Angles?

**EXPLANATION**

If two Angles are Supplementary, then their sum of measure is 180˚

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

Sum of Supplementary Angles = 180˚

( 1a )˚ + (4a )˚ = 180˚

( 5a )˚ = 180˚

a =

a = 36

Hence, measure of two Angles are:

( 1a )˚ = ( 1 x 36 )˚ = 36˚

( 4a )˚ = ( 4 x 36 )˚ = 144˚

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