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Polygon Angles Level 3

Practise the skills of finding interior and exterior angles of polygons to answer these questions.

Level 1 Level 2 Level 3 Exam-Style Description Reminders More Angle Activities

You can earn a trophy if you get at least six questions correct.

1. An exterior angle of a regular polygon is 20°. How many sides does the polygon have? Correct Wrong

2. An interior angle of a regular polygon is 150°. How many sides does the polygon have? Correct Wrong

3. Calculate the size of an interior angle of a regular heptagon (seven-sided polygon). Give your answer to one decimal place. Correct Wrong

4. Find the value of a in the diagram below:
Diagram
Correct Wrong

5. Find the value of b in the diagram below:
Diagram
Correct Wrong

6. Find the value of d in the diagram below of a triangle drawn from the vertices of a regular nonagon:
Diagram
Correct Wrong

7. Calculate the size of angle ABC in this diagram of four regular hexagons surrounding a square.
Diagram
Correct Wrong

8. Find the value of c in the diagram below of a regular pentagon joined to a square:
Diagram
Correct Wrong

9. Three irregular pentagons fit together without leaving any space as shown in this exploded diagram. Each pentagon has two right angles and one line of symmetry. Calculate the value of the marked angle.
Diagram
Correct Wrong

10. Find the value of w in the diagram below of a regular pentagon sharing two vertices with a regular heptagon. Give your answer to one decimal place.
Diagram
Correct Wrong

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This is Polygon Angles level 3. You can also try:
Level 1 Level 2

Here are some related exercises:
Angles in Triangles Angle Points Angles in Parallel Lines Angles in Circles

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Featured Activity

Nine Digits

Nine Digits

Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Description of Levels

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Level 1 - Name and find the size of the angles in regular polygons.

Level 2 - Find the size of the angles marked with letters in simple diagrams.

Level 3 - A mixture of problems related to the angles in polygons.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Angle Activities including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Reminders

All Polygons

The sum of the exterior angles of any polygon is 360°.

The sum of the interior angles of an n-sided polygon is 180(n − 2)°.

Regular Polygons

Each exterior angle of an n-sided regular polygon is 360° ÷ n

Each interior angle of an n-sided regular polygon is 180° − 360° ÷ n

Interior and exterior angles

Interactive animation showing why exterior angles add up to 360°

Other angle theorems

Circle theorems

More angle activities

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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