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Calculate Missing Interior Angles of Polygons

In this worksheet, students will use a rule to calculate missing angles in irregular polygons.

'Calculate Missing Interior Angles of Polygons' worksheet

Key stage:  KS 3

Year:  Year 8 Maths worksheets

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Apply Facts About Angles and Sides

Difficulty level:  

Worksheet Overview

In this activity, we will calculate the missing angles inside irregular polygons.


An irregular polygon does not have all the same angles and sides unlike a regular polygon. 


Regular hexagon                  Irregular hexagon


The Sum of the Interior Angles of any Polygon:


rule of sum of interior angles


Therefore, we can work out the sum of angles of any polygon using this rule!


Let's try a question!



Calculate the sum of the interior angles in a heptagon.


a heptagon



We know that a heptagon has seven sides.


a heptagon


It splits into five triangles (5 x 180) or we can use our rule:



Sum = 180 x (7 sides - 2)

Sum = 180 x 5

Sum = 900o


woman writing

Let's do some questions!

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