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Polygon Angles Level 3

Use your ability to find internal and external angles of polygons to answer these questions.

Level 1 Level 2 Level 3 Level Descriptions Reminders Exam Questions 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 24°. 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 c in the diagram below of a regular pentagon joined to a square:
Diagram
Correct Wrong

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

8. 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 Level 3. You can also try: Level 1 | Level 2 | Angles in Triangles | Points | Parallel Lines.

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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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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Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

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"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Featured Activity

Tran Tunnels

Tran Tunnels

Answer the questions as you find your way through the tunnels. Collect coins on the way. There's a musical theme to this adventure game and you won't be able to complete it unless you solve all of the clues.

Answers

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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:

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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.

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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