Polygon Angles Level 3

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

Level 1Level 2Level 3Exam-StyleDescriptionRemindersMore 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? 2. An interior angle of a regular polygon is 162°. How many sides does the polygon have? 3. Calculate the size of an interior angle of a regular heptagon (seven-sided polygon). Give your answer to one decimal place. 4. Find the value of a in the diagram below: 5. Find the value of b in the diagram below: 6. Find the value of d in the diagram below of a triangle drawn from the vertices of a regular nonagon: 7. Calculate the size of angle ABC in this diagram of four regular hexagons surrounding a square. 8. Find the value of c in the diagram below of a regular pentagon joined to a square: 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. 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.
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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.

Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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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 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Shunting Puzzles

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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

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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.

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

Interactive animation showing why exterior angles add up to 360°

Other angle theorems

Circle theorems

More angle activities

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