Polygon Angles Level 3

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

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 1. An exterior angle of a regular polygon is 24°. How many sides does the polygon have? 2. An interior angle of a regular polygon is 160°. 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

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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.

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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 (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

Interactive animation showing why exterior angles add up to 360°

Other angle theorems

Circle theorems

More angle activities

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