Today in the chapter we read about all the Angles. In this chapter, we discuss the definition of all the angles and types of angles. There are many types of angles like complementary angles, obtuse angles, right angles, complementary and supplementary angles, etc. we also read that a 45-degree angle is called an acute angle. A 45-degree angle is a very common angle.

This is a very important topic in terms of exams. Our expert aims that learners properly understand the topic. We also discuss the difference between complementary and supplementary angles Knowledge of angles is very important in life. Soon we provide his chapter PDF.

**Angle**

**What is an angle? Definition of an angle? Define the angle?**

**Definition of the angle:** Where two simple straight lines meet one another, that place is called an angle.

**OR**

When two lines intersect, at the point of their intersection an angle is formed. The two rays that form the angle are known as the sides of the angle.

**Unit of Measurement of Angle**

The unit of measuring unit is Degree (°). Angles are measured in degree.

**Symbol of Angle:** The angle symbol is ∠. We represent angle from ∠.

The point where the angle is formed, that point always kept in the middle. When we write the name Angle.

like this: ∠A

**B**C

the above figure has two lines AB and BC, where these lines intersect each other to form an angle. Which middle point is B.

**Types of Angles**

There are various types of angles based on their measure of the angle. Types of angles are given below :

*1. Right Angle*

*2. Acute Angle*

*3. Obtuse Angle*

*4. Straight Angle*

*5. Reflex Angle*

*6. The Whole Angle*

**1. Right Angle**

*“An angle of exact 90 degree, is called Right angle.”*

It mean when two lines are perpendicular then they makes 90 degree angle (Right Angle).

The value of Right Angle : Value of Right Angle is always fixed. Means we can say –

Right Angle = 90°

In the above figure line MN and NO are perpendicular, which are formed 90° angle.

∠MNO is a Right Angle

∠MNO = 90°

**2. Acute Angle**

*“An angle which are smaller than 90 degree is called Acute Angle.”*

Acute Angle Value : Acute Angle value range between 0 degree to 90 degree.

The value of Acute Angle : Value of Acute Angle are between 0 degree to 90 degree. Means we can say –

Acute Angle = Greater than 0° – Less than 90°

0° < Acute Angle < 90°

∠XYZ is a Acute Angle.

0° < ∠XYZ < 90°

**3. Obtuse Angle**

*An angle which are greater than 90 degree is called Obtuse Angle.*

Obtuse Angle Value : Obtuse Angle value range between 90 degree to 180 degree.

The value of Obtuse Angle : Value of Obtuse Angle are between 90 degree to 180 degree. Means we can say –

Obtuse Angle = Greater than 90° – Less than 180°

90° < Obtuse Angle < 180°

90° < Obtuse Angle < 180°

∠KLM is a Obtuse Angle.

90° < ∠KLM < 180°

**4. Straight Angle**

*An angle of exact 180 degree, is called Straight angle.*

The value of Straight Angle : Value of Straight Angle is always fixed. Means we can say –

Straight Angle = 180°

Straight Angle = 180°

∠EFG is a Straight Angle.

∠EFG = 180°

**5. Reflex Angle**

*An angle which is Greater than 180° and smaller than 360°, called Reflex Angle.*

The value of Reflex Angle : Value of Reflex Angle are between 180 degree to 360 degree. Means we can say –

Reflex Angle = Greater than 180° – Less than 360°

180° < Reflex Angle < 360°

180° < Obtuse Angle < 360°

∠PQR is a Reflex Angle.

180° < ∠PQR < 360°

**6. The Whole Angle**

*The angle of 360 degree is called Whole Angle.*

The value of Whole Angle : Value of Whole Angle is always fixed. Means we can say –

Whole Angle = 360°

**Other Types of Angles**

Now we read about other types of angles like Complementary Angles etc. There is types of angles given below –

1. Complementary Angle

2. Supplementary Angle

**1. Complementary Angle**

*A pair of angles whose sum are equal to 90 degrees is called, Complementary Angle.*

In the above figure 1 we can see both angle sum are 90 degree. So both are Complementary Angle of each other. So we can say

∠XYZ + ∠ABC = 90° (Complementary Angle)

50° + 40° = 90°

Example) : 50° + 40° = 90°

45° + 45° = 90°

60° + 30° = 90°

**2. Supplementary Angle**

*A pair of angles which sum are equal to 180 degree called Supplementary Angle.*

In the above figure we can see both angle sum are 180 degree. So both are Supplementary Angle of each other. So we can say

∠MNO + ∠PQR = 1800° (Supplementary Angle)

70° + 110° = 90°

Example : 150° + 30° = 180°

90° + 90° = 180°

120° + 60° = 180°

**When two parallel lines intersect a transversal line, the following angles are formed on that line.
1. Alternate Angle
2. Vertically Opposite Angle
3. Corresponding Angle
4. Adjacent Angles
5. Linear Pair**

**1. Alternate Angles
**When two parallel lines intersect by an transversal line, the angles that form the opposite direction of the transversal line are called the Alternate angles.

The easiest way to find alternate angles is to identify a “Z” on transversal line.

Alternate Angles value are same if these are formed on parallel lines.

In the above figure same colors angle are Alternate angles. Like this

* Interior Alternate Angles are –*∠4 and ∠6 are Alternate angles

∠3 and ∠5 are Alternate angles

*Exterior Alternate Angles are –*∠1 and ∠7 are Alternate angles

∠2 and ∠8 are Alternate angles

**2. Vertically Opposite Angles
**When two lines intersect each other then the angle which are opposite to each other is called Vertically Opposite Angles.

If the two lines intersect each other, then Vertically Opposite Angles are formed are always equal.

In the above figure we can see that two line l and m intersect each other on point O and formed 4 angles in which Vertically Opposite Angles are same colors angles.

∠1 and ∠3 Vertically Opposite Angles (∠1 = ∠3 always equal)

∠2 and ∠4 Vertically Opposite Angles (∠2 = ∠4 always equal)

**3. Corresponding Angles
**Angles which are present in a similar position are called Corresponding Angles.

If Corresponding Angles are formed on parallel lines then these are always equal to one another.

The easiest way to find Corresponding Angles is to identify a “F” on transversal line.

In the above figure we can see the same colors angles, which are Corresponding Angles. These are always equal. These angles are –

∠1 and ∠5 are Corresponding Angles, ∠1 = ∠5

∠2 and ∠6 are Corresponding Angles, ∠2 = ∠6

∠4 and ∠8 are Corresponding Angles, ∠4 = ∠8

∠3 and ∠7 are Corresponding Angles, ∠3 = ∠7

**4. Adjacent Angles
**A pair of angles that have at least a side and a vertex common, called Adjacent Angles.

Adjacent Angles have common side and a common vertex but endpoint are not common.

In the above figure we can see Adjacent Angles, which are besides each other.

In figure Common vertex is B and Common side is BC. Then,

∠ABC and ∠CBD are Adjacent Angles.

**5. Linear Pair
**A pair of angles formed on a straight line is called a Linear Pair.

A linear pair is, a pair of adjacent angles, whose sides which are not common are opposite.

A linear Pair Angles sum are always 180 degree.

In the above figure there are 3 angles formed on a straight line, which sum are 180 degree.

So ∠ABE + ∠EBD + ∠DBC = 180°

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