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Calculate Angles Around Polygons

In this worksheet, students will use angle rules to calculate the angles around a polygon.

'Calculate Angles Around 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 angles around polygons.


A polygon is the collective name for all the shapes that have straight sides!


mixture of polygons


The outside - exterior angles of any polygon add up to 360o


exterior angles of polygons


A regular polygon has all the sides and angles the same.

Therefore, we can work out one of the exterior angles of any regular polygon!



Calculate the exterior  angles of a regular hexagon.


a hexagon



We know that a regular hexagon has six sides.


exterior angles of a hexagon


We also know that all the exterior angles add up to 360o

To find one angle, we can divide 360 by the number of sides.

360 ÷ 6 sides = 60o


Each exterior angle = 60o


green tick


This helps us to find the interior (inside) angle too!

The interior + exterior angle = 180 a straight line!


Look here!


angles in a polygon


You can see a zoomed-in angle from the triangle, square, pentagon and hexagon from above.

The dot is the interior angle. 

You can see that the interior + exterior angle = 180o


man thumbs up


Let's do some polygon questions!

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