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Find Internal and External Angles in Polygons

In this worksheet, students will find internal and external angles of regular polygons and solve related problems.

'Find Internal and External Angles in Polygons' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions Angles

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

What is your favourite computer game?

How long do you spend playing it?

 

Do you know that calculating angles is extremely important within computer games and graphics?

 

Interior and exterior angles are used in compiling 3D graphics.

 

Lets remind ourselves how we can calculate both these types of angles. 

 

 

Diagram of interior angles in a polygon

Rule for finding internal angles = Number of sides - 2 × 180 ÷ number of sides

 

 

e.g Find the value of interior angles of the pentagon shown above. 

 

5 - 2 = 3

3 × 180 = 540° in total within the pentagon

540 ÷ 5 = 108° internal angle

 

 

 

Let's investigate the relationship between the interior and exterior angles now.

 

e.g. Find the value of the exterior angle of the pentagon shown below. 

 

Diagram showing exterior angles

 

 

If we place an interior angle next to its exterior counterpart, they will create a straight line

We know that there are 180° in total in a straight line. 

So if we know either one of the interior or exterior angles, we can use this to find its counterpart. 

 

Diagram showing relationship between interior and exterior angles

 

 

 

Let's put these rules into practice now using a new example. 

 

e.g. Find the interior and exterior angle of this heptagon.

A green heptagon

To find the value of the interior angles:

7 - 2 = 5

5 × 180 = 900

900 ÷ 7 = 128.5°

 

To find the value of the exterior angles:

360 ÷ 5 = 51.5°

 

Let's check that these two angles add together to make 180° (value in a straight line): 

128.5° + 51.5° = 180°

 

 

 

Fabulous - it's time to get off the computer games and get to work now!

 

In this activity, we will use the rules illustrated above to calculate the interior and exterior angles of regular polygons with a variety of different sides. We will also use these formulae to find the number of sides of a shape or solve related problems. 

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