In this section we discuss about **different types of angles pairs** like* Complementary Angles, **Supplementary **Angles, Conjugate Angles & Congruent angles* with examples

### Angle Pairs Definition and Examples | Conjugate and Congruent Angles

Contents

For Basic concepts of angles and Different Types of Angles in Geometry like Zero Angle, Acute Angle, Right Angle, Obtuse angle, Straight Angle, Reflex Angle & Complete angle go through the below link

Acute, Right, Obtuse, Straight, Reflex & Complete angle

### Complementary Angles

If the sum of two angles are 90^{o} then the angles are said to be *Complementary angles*. Each one of these angles is called the *Complementary* of the other.

Example:

From the above example ∠POR = 50^{o} , ∠ROQ = 40^{o } are *complementary angles*

Since sum of the these two angles are 90^{o}

i.e ∠POR + ∠ROQ = 50^{o} + 40^{o} = 90^{o}

Here ∠POR is said to be __complementary angle__ of ∠ROQ and ∠ROQ is said to be __complementary angle__ of ∠POR.

*How to find complementary angles*

If any angle of ‘ y ‘ is less than **90 ^{o}** then

Complementary angle of **y = 90 ^{o} – y^{o}**

### Supplementary angles

If the sum of two angles are 180^{o} then the angles are said to be* supplementary angles*, . Each one of these angles is called the supplementary of the other.

Example:

From the above example ∠POR = 50^{o} , ∠ROQ = 130^{o } are *supplementary angles*

Since sum of the these two angles are 180^{o}

i.e ∠POR + ∠ROQ = 50^{o} + 130^{o} = 180^{o}

Here ∠POR is said to be supplementary angle of ∠ROQ and ∠ROQ is said to be supplementary angle of ∠POR.

*How to find supplementary angles*

If any angle of Y is less than 180^{o} then

Supplementary angle of **y = 180 ^{o} – y^{o}**

### Conjugate Angles:

If the sum of two angles are 360 then the angles are said to be Conjugate angles, . Each one of these angles is called the conjugate of the other.

Example:

From the above example ∠POR = 50^{o} , ∠ROQ = 310^{o } are conjugate angles

Since sum of the these two angles are 360^{o}

i.e ∠POR + ∠ROQ = 50^{o} + 310^{o} = 310^{o}

Here ∠POR is said to be conjugate angle of ∠ROQ and ∠ROQ is said to be conjugate angle of ∠POR.

*How to find conjugate angles*

If any angle of ‘y ‘ is less than 360^{o} then

Conjugate angle of **y = 360 ^{o} – y^{o}**

### Congruent angles:

Two angles having the same measure are known as congruent angle.

In the above figure ∠AOB & ∠POQ are congruent angles.

Since ∠AOB = ∠POQ = 60^{o}

### Angular bisector:

A ray which divides an angle into two congruent angles is called angular bisector.

Example:

In the above figure ray OR is called angular bisector of ∠POQ.

Since ∠POR = ∠ROQ = 30^{o}

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