Sum of angles of polygon
This is a sample digital text prepared as part of 4th semester B.Ed. ICT workshop.
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
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
A 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°
PowerPoint
Video
Practice Questions
https://quizzory.in/id/629478f7e24bfa7b4d398258
References
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