In this section we know about **definition of angle in geometry** and its types of angles like *Interior and Exterior of an angle*, *Zero Angle, Acute Angle, Right Angle, Obtuse angle, Straight Angle, Reflex Angle & Complete angle*

*What is Angle*

An angle is formed when two rays originate from same end point. The two rays formed an angle are called** ‘arms or ‘sides ‘** of the angle and the end point is called the **vertex** of the angle.

An angle is denoted by the symbol** ” ∠ “**

Here the rays OP, OQ from an angle denoted by **∠POQ** or **∠QOP.**

Sometimes, the above angle by written by the letter at the *vertex of the angle*. For example , in the above figure the angle **∠POQ** is also denoted by “** ∠O** ” or** angle O**

In the above figure angles are named as follows

**∠POR , ∠POQ & ∠ROQ**

The standard unit for measuring an angle is **degree.**

Degree is defined as 360^{th} part of one complete revolution.

One complete revolution is equal to 360 degree or 360^{o}

One degree is further divided into 60 equal parts. Each equal part is called one** minute** and it is written as 1′

**1 ^{o} = 60′**

One minute is further divided into 60 equal parts. Each equal part is called one** second** and it is written as 1″

**1′ = 60″**

Contents

## Angles in Maths | Acute, Right, Obtuse, Straight, Reflex & Complete angle

### Interior and Exterior of an angle

**Interior of an angle :** The part of the plane which is within the arms of an angle produced indefinitely is called the* interior of the angle.*

**Exterior of the angle:** The part of the plane which is outside the arms of an angle produced indefinitely is called the *exterior of the angle.*

**For example:**

In the above figure all points in the plane of **∠POQ** can be divided into three regions

*On the angle* : The points on the angle are **P, Q & R**

*Interior of the angle :* The points in the interior **– C & D**

*Exterior of the angle :* The points in the exterior – **A, B & E**

**Types of Angles:**

### Zero Angle

The angle is formed by initial and final position of a ray coincide without making any revolution. Thus whose measure is O^{o} is called* zero angle.*

**For example:**

In the above figure ∠POQ = Zero angle = O^{o}

### Acute Angle

The angle whose measure is less than 90^{o} is called an *acute angle.* It is also defined as ” An angle which is greater than zero angle bust less a *right angle* is called an __acute angle__.

For example 35^{o} , 40^{o} , 60^{o} , 70^{o} . . . . . etc are **acute angles.**

In the below figure ∠POQ is called *acute angle.*

### Right Angle

The *right angle* is defined as ” If the initial position of the ray OP is horizontal and it rotates to occupy vertical position OQ then we say that angle formed is a __right angle __.

Thus , the angle whose measure is 90^{o} is called *right angle*.

### Obtuse angle

The angle whose measure is greater than 90^{o} but less than 180^{o} is called *obtuse angle.*

For example 95^{o} , 100^{o} , 120^{o} , 170^{o} . . . . . etc are **Obtuse angle**.

In the below figure ∠POQ is called __Obtuse angle__.

### Straight Angle

The *straight angle* is formed when the initial and final position of a rotating ray opposite to each other.

The angle by two opposite rays OP and OQ is a straight angle since they form a straight line PQ and this is half of one complete angle.

Thus ∠POQ = 180^{o} = Straight angle.

### Reflex Angle

The angle whose measure is more than 180 o and less than 360o is called** reflex angle.**

For example: 200^{o} , 250^{o} , 300^{o} , 350^{o} . . . . etc are **reflex angles.**

In the below figure ∠POQ is called __Reflex angle__.

### Complete angle

The angle is said to be complete angle, If an angle id formed by rotation ray, after making a complete revolution, coincides with the initial position.

Thus, the angle whose measure is 360^{o} is called **complete angle**.

In the above figure, the arm OP coincide with the arm OQ after making complete revolution.

Therefore, ∠POQ = 360^{o} = Complete angle.

Please go through the below link regarding **complementary and supplementary angles meaning with examples**

C**omplementary and supplementary angles
**

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