CLASS - VIII -17

ONLINE MATHS CLASS - VIII - 18 ( 11 / 09 /2020)

We discussed different types of polygons in the last class .

Polygon Number of Number of Number of
sides
vertices angles

Triangle 3 33

Quadrilateral 4 44
Pentagon 5 55
Hexagon 6 66

Heptagon 7 77

Octagon 88 8

SARATH .A .S , HST ,GHS ANCHACHAVADI

Sum of the angles of polygons
Triangle is the simplest polygon . It has three sides and three angles .

Sum of the angles of a triangle is 180 º

Sum of the angles of a quadrilateral
If we join two triangles as shown in the figure we get

a quadrilateral .

Consider the quadrilateral ABCD .

Draw diagonal AC

Sum of the angles of the quadrilateral ABCD

= Sum of the angles of the triangle ABC + Sum of the angles

of the triangle ACD

= 180 º + 180 º

= 360 º

Number of sides of a quadrilateral = 4

Number of triangles obtained while drawing a diagonal = 2

Sum of the angles of a quadrilateral = 2 x 180 º = 360 º

Sum of the angles of a quadrilateral is 360 º

Sum of the angles of a pentagon

If we join a triangle to a quadrilateral , we get a pentagon
as we saw in the last class . That is if we join three triangles
as shown in the figure , we get a pentagon .
That is sum of the angles of the pentagon is the sum of these
three triangles .

SARATH .A .S , HST ,GHS ANCHACHAVADI

Number of sides of a pentagon = 5
Number of triangles obtained while drawing all diagonals from one vertex = 3
Sum of the angles of a quadrilateral = 3 x 180 º

= 540 º
Sum of the angles of a pentagon is 540 º

Sum of the angles of a hexagon

If we join a triangle to a pentagon , we get a hexagon
as we saw in the last class . That is if we join four triangles
as shown in the figure , we get a hexagon .
That is sum of the angles of the hexagon is the sum of these
four triangles .
Number of sides of a hexagon = 6
Number of triangles obtained while drawing all diagonals from one vertex = 4
Sum of the angles of a quadrilateral = 4 x 180 º

= 720 º

Sum of the angles of a hexagon is 720 º

If we continue like this , what will be the sum of the angles of a heptagon ?
Number of sides of a heptagon = 7
Number of triangles obtained while drawing all diagonals from one vertex = 5
Sum of the angles of a heptagon = 5 x 180 º

= 900 º

SARATH .A .S , HST ,GHS ANCHACHAVADI

NB :
Number of triangles obtained while drawing maximum number of diagonals from one vertex
of a polygon is 2 less than its number of sides .

Polygon Number of sides Maximum Number of Sum of the angles
number of triangles
Triangle 3 diagonals
Quadrilateral 4 drawing from 1 1 x 180 = 180 º
5 one vertex 2 2 x 180 = 360 º
Pentagon 6 3 3 x 180 = 540 º
Hexagon 7 0 4 4 x 180 = 720 º
Heptagon 8 5 5 x 180 = 900 º
Octagon 9 1 6 6 x 180 = 1080 º
Nonagon 10 7 7 x 180 = 1260 º
Decagon 2 8 8 x 180 = 1440 º

3

4

5

6

7

Sum of angles of a polygon having n sides is (n– 2 ) 180º

Let's solve some problems related to this
1. What is the sum of the angles of a 52 sided polygon ?
Answer .
Number of sides = 52
Number of triangles = 52 – 2 = 50
( Here we consider the number of triangles obtained while drawing maximum number of

SARATH .A .S , HST ,GHS ANCHACHAVADI

diagonals from one of its vertex )
Sum of angles = 50 x 180 = 9000 º
2. The sum of the angles of a polygon is 8100º . How many sides does it have ?
Answer .
Sum of the angles = 8100º
Number of triangles x 180 = 8100º
Number of triangles = 8100 = 45

180
Number of sides = 45 + 2 = 47
More activities ( Text book page 50 )

SARATH .A .S , HST ,GHS ANCHACHAVADI