Concept of Angle and its types

In this post we will discuss the concept of angle and the different type of angle formation. In order to understand geometry it is very important to have clear concept of angles, that’s why we have made an effort to develop materials which is easy to understand.

Concept of Angles

What are angles?

An angle is formed when two rays are joined together at a common point. The angle is represented by the symbol ‘’.
Angles are generally measured in degrees.

How angle is formed?

Angle formation is very easy process.
Take two rays and join them at the common point after which you will get an angle.
Have a look at the following illustration

definition of angle

Parts of an angle

Node or Vertex – The common point is called node or vertex

Arms of the angle – The two rays are called arms of the angle.

Initial side is the reference side. All measurements are done using this side. The other side is terminal side.

Parts of Protractor

Protractor is a tool with the help of which you can easily find the angle between two line. The tool can be easily found at the local stationary shop and cheap price

what is protractor in maths

How to measure an angle

To measure angle i.e., ∠AOB:

Step 1: Place the center point of the protractor on the vertex O.
Step 2: Adjust the base line of the protractor so that it is aligned with the line OB
Step 3: Read the value of angle AOB, from the inner scale.

Different Types of Angles

Angles are classified into different types, some of the notable distinctions is given below

1.Acute angle
2. Right angle
3. Obtuse angle
4. Straight angle
5. Reflex angle
6. Complete angle

types of angles in geometry

Acute Angle – Angle whose measure is less than 90o is called acute angle

what is a acute angle

Right Angle – Angle whose measure is equal to 90o is called right angle

what is right angle

Obtuse Angle – Angle whose measure is greater than 90o but greater than 180o is called obtuse angle.

what is obtuse angle

Straight Angle – Angle whose measure is equal to 180o is called straight angle.

what is straight angle

Reflex Angle – Angle whose measure is greater than 180o but less than 360o is called reflex angle

what is reflex angle

Complete Angle – Angle whose measure is equal to 360o is called complete angle.

what is complete angle

Important Properties of Angles

In this topic we will understand some important properties of angles which will be helpful to solve geometry questions in the future. Try to remember these points because they are important for your exams

Complementary Angles

If the sum of angles is equal to 90o then the angles are called complementary angles

what are complementary angles

∠AOC and ∠BOC are complementary angles

Supplementary Angles

If the sum of angles is equal to 180o then the angles are called supplementary angles

what are supplementary angles

∠AOC and ∠BOC are supplementary angles

Adjacent Angles

Two angles with a common side and a common vertex are called adjacent angles

what are adjacent angles

∠1 and ∠2 are adjacent angles

Vertically opposite angles

Angles that have a common vertex and whose sides are formed by the same line are called vertically opposite angles. Vertically opposite angles are equal in measure

what are vertically opposite angles

(∠1 & ∠3) and (∠2 & ∠4) are vertically opposite angles

Alternate interior angles

Alternate interior angles are equal in measure. They are formed when two parallel lines are intersected by a transversal.

what are alternate interior angles

(∠1 & ∠3) and (∠2 & ∠4) are alternate interior angles

Alternate exterior angles

Alternate exterior angles are equal in measure. They are formed when two parallel lines are intersected by a transversal

(∠1 & ∠3) and (∠2 & ∠4) are alternate exterior angles

Corresponding Angles

Angles which are in the same position in the figure when two parallel lines are intersected by transversal
Corresponding angles are equal in measure.

what are corresponding angles

In the above figure, angle (2 & 3) are corresponding angles because they are in same position.
Similarly angle (1&4), (5&7) (8 & 6 ) are corresponding angles and are equal in measure

Positive Angle

An Angle measured in Anti-Clockwise direction is Positive Angle

What is a positive angle

Negative Angle

An angle measured in Clockwise direction is Negative Angle

what is a negative angle

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