Transum Software

Polygon Angles Level 3

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

  Menu   Level 1 Level 2 Level 3 Mixed Exam-Style Help 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 156°. 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

Check

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.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London:

"I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Without Lifting

Without Lifting

Can you draw these diagrams without lifting your pencil from the paper? This is an interactive version of the traditional puzzle. Some diagrams are possible while others are not. What is the rule?

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.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

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:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

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.

Apple

©1997-2024 WWW.TRANSUM.ORG

Description of Levels

Close

Close

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.

Log in Sign up

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 (180n − 360)°.

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.

Close

Close