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Interior Angle Sums

In this worksheet, students calculate the sum of the interior angles of the given polygons.

'Interior Angle Sums' worksheet

Key stage:  KS 2

Year:  Year 5 11+ worksheets

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   2D Shapes: Circles, Angles and Bearings

Difficulty level:  

Worksheet Overview

 You already know that the interior angles of a triangle add up to 180º.


Polygons with more sides have a larger sum of interior angles.

To work out the sum of the interior angles of a polygon with more sides, we choose one of the corners and split the polygon into triangles.  Each triangle will contain 180°.



Work out the sum of the interior angles of this hexagon.




Choose any one corner.



Draw diagonals from the chosen corner to form triangles.



There are 4 triangles inside the hexagon.

4 x 180° = 720°


The sum of the interior angles of a hexagon is 720°.


General Rule:

When you have a shape with n sides, the number of triangles it can be split into is n-2

Once you have the number of triangles, we can simply multiply that by 180° to find the internal angles.

For example: A 5 sided shape can be split into 3 triangles, if you then multiply 3 by 180 you get that there are 540° in a 5 sided shape.



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