Sum of angles of polygon

 This is a sample digital text prepared as part of 4th semester B.Ed. ICT workshop.

Digital Text

NSS TRAINING COLLEGE

OTTAPALAM

ICT WORKSHOP

DIGITAL TEXT

Name of the teacher  : Harsha S

Date   : 25/05/2022

Department   : Mathematics

Class   : 8

Subject   : Mathematics

Duration   : 30 minutes

Unit   : Polygons

Topic   : Sum of angles


Sum of Angles of Polygon


Objectives

  • To understand about different polygons

  • To determine the relationship among sides, angles and diagonals

     of different polygons
  • To understand about sum of interior angles of polygon

  • To solve real life problems

Polygon DefinitionA Polygon is a two-dimensional geometric figure that has a finite

number of sides. The sides of a polygon are made of straight line

segments connected to each other end to end. Thus, the line segments

of a polygon are called sides or edges. The point where two line

segments meet is called vertex or corners, henceforth an angle is

formed. Thus, a Polygon is a closed figure made up of line segments

(not curves) in a two-dimensional plane. Polygon is the combination

of two words, i.e, poly (means many) and gon (means sides).

A minimum of three line segments is required to connect end to end,

to make a closed figure. A polygon with a minimum of three sides is

known as Triangle and it is also called 3-gon.

Polygon shape and properties

Triangle

A Triangle is a three-sided polygon that consists of three edges and

three vertices. Thus, a triangle is a 3-sided Polygon sometimes

(but not very commonly) called the trigon. Every triangle has three

sides and three angles, some of which may be the same.

Quadrilateral

A Quadrilateral is a polygon having four sides, four angles, and four vertices.

The word ‘quadrilateral’ is derived from the Latin words ‘quadri’,

which means four, and ‘latus’, which means side.

Quadrilaterals can be classified into Parallelograms, Squares,

Rectangles, and Rhombuses. Square, Rectangle, and Rhombus are

also Parallelograms.

Pentagon

A Pentagon is a geometrical shape, which has five sides and five angles. Here

“Penta” denotes five and “gon” denotes angle. Thus, the word

“pentagon” comes from the Greek word “pentagonos”, which means

“five-angled”.

Hexagon

Hexagon is defined as a closed 2D shape that is made up of six straight lines.

It is a two-dimensional shape with six sides, six vertices, and six

interior angles. The name is divided into 'hex', which means six, and

'gonia', which means corners.

Polygons

An n-sided polygon is called n-gon.

Sum of Interior angles of polygon

The sum of interior angles of a triangle is equal to 180 degrees.

When we start with a polygon with four or more than four sides,

we need to draw all the possible diagonals from one vertex.

The polygon then is broken into several non-overlapping triangles.

The angle sum of this polygon for interior angles can be determined

on multiplying the number of triangles by 180°.

Triangle

Sum of angles = 180°

Quadrilateral:

Number of triangles = 2

Sum of angles = Sum of angles of 2 triangles

= 180° + 180°

= 2 180°

= 360°

                   


Pentagon:

Number of triangles = 3

Sum of angles = Sum of angles of 3 triangles

= 180° + 180° + 180°

= 3 180°

= 540°

             


Hexagon:

Number of triangles = 4

Sum of angles = Sum of angles of 4 triangles

= 180° + 180° + 180° + 180°

= 4 180°

= 720°

           


Heptagon:

Number of triangles = 5

Sum of angles = Sum of angles of 5 triangles

= 180° + 180° + 180° +180° + 180°

= 5 180°

= 900°

               


Octagon:

Number of triangles = 6

Sum of angles = Sum of angles of 6 triangles

= 180° + 180° + 180° + 180° + 180° + 180°

= 6 180°

= 1080°

             


Polygon:

Number of sides = n

Number of triangles = n - 2

Sum of angles = Sum of angles of (n - 2) triangles

= (n - 2) 180°

Polygon Name

Number of Interior Angles

Number of 

Triangles

Sum of Interior 

Angles 

Triangle

3

1

1 x 180°  = 180°

Quadrilateral

4

2

2 x 180°  = 360°

Pentagon

5

3

3 x 180° = 540°

Hexagon

6

4

4 x 180°  = 720°

Heptagon

7

5

5 x 180°  = 900°

Octagon

8

6

6 x 180°  = 1080°

Nonagon

9

7

7 x 180°  = 1260°

Decagon

10

8

8 x 180°  = 1440°

Polygon

n

n-2

(n-2) x 180° 


The sum of the angles of an n-sided polygon is n-2×180°.


PowerPoint 

Sum of angles ppt


Video



https://youtu.be/schvQUgUEAQ


Practice Questions

https://quizzory.in/id/629478f7e24bfa7b4d398258

References

  1. SCERT Kerala State Syllabus 8th Standard Maths

  2. Byjus .com

  3. Wikipedia

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