Finding the Sum of a Polygon’s Interior

Angles

Apr 19, 2023

Here are some polygons

The word ‘polygon’ is

a Greek word.

PolyPoly means many

and gongon means angles.

Triangle

Pentagon

Octagon

a

b

c

ed

How to find the sum of the interior angles – i.e. How to find a + b + c + d + e

How to find the sum of the interior angles – i.e. How to find a + b + c + d + e

Split the shape up into triangles

How to find the sum of the interior angles – i.e. How to find a + b + c + d + e

Split the shape up into triangles

Each triangle contains 1800

18001800

1800

How to find the sum of the interior angles – i.e. How to find a + b + c + d + e

Split the shape up into triangles

Each triangle contains 1800

3 x 180 = 54001800

1800

1800

How to find the sum of the interior angles – i.e. How to find a + b + c + d + e

Split the shape up into triangles

Each triangle contains 1800

3 x 180 = 5400

The sum of the interior angles is 5400

18001800

1800

Name Number of Sides

Sum of Interior Angles

Quadrilateral 4

Pentagon 5

Hexagon 6

Heptagon 7

Octagon 8

Nonagon 9

Decagon 10

Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.

Name Number of Sides

Sum of Interior Angles

Quadrilateral 4 360

Pentagon 5 540

Hexagon 6 720

Heptagon 7 900

Octagon 8 1080

Nonagon 9 1260

Decagon 10 1440

Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.

1200

Interior Angle

NB. If the polygon is regular, to find an interior angle use the rule:

Int.Angle = 180 – (360 ÷ n)

n is the number of sides

Int. = 180 – (360 ÷ 6) 180 – 60 =120

Regular Polygons

1200

Interior Angle

NB. If the polygon is regular, to find an exterior angle use the rule:

Ext.Angle = 360 ÷ n

n is the number of sides

And Ext. Angle = 180 – Int.Angle

Regular Polygons

exterior angle (180 – 120 = 60