47 self-marking GCSE and IGCSE practice questions on Angles in polygons, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Instant marking with full worked solutions on every question.
A few of the 47 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 2-3
Work out the sum of the interior angles of a heptagon (a polygon with 7 sides).
Show the worked solution
Sum of interior angles = (7−2)×180 = 5×180 = 900°
What are the common mistakes in Angles in polygons?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Forgets to subtract 2 from the required value (e.g. number of diagonals/interior angle formula step)
Used n × 180 instead of (n-2) × 180; forgot to subtract 2 from the number of sides
Subtracts 1 where 2 should have been subtracted (e.g. in a formula requiring -2)
Used (n-1) × 180 instead of the correct formula (n-2) × 180
Uses 180° where 360° was the correct total for the configuration
Used 180° instead of 360° as the total for the exterior angles of a polygon
Quick answers about Angles in polygons
How many Angles in polygons practice questions are there?
There are 47 self-marking GCSE and IGCSE Maths questions on Angles in polygons, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Each one is marked instantly and has a full worked solution.
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No. You can start practising Angles in polygons straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
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Question 22 marksGrade 4
(a) Work out the size of an exterior angle of a regular hexagon.
(b) Use your answer to part (a) to write down the size of an interior angle of a regular hexagon.
Show the worked solution
Exterior angle =360÷6=60°. Interior and exterior angles are supplementary, so interior angle =180−60=120°. B1B2
Question 33 marksGrade 5
A square, a regular hexagon and part of another regular polygon meet at a point P, exactly filling the angle around the point.
Find the number of sides of the other regular polygon.
Question 43 marksGrade 6-7
Each exterior angle of a regular polygon is 9°. Work out the number of sides the polygon has. Show your working.
Question 53 marksGrade 7
Angle BAE is the interior angle at vertex A of a regular 18-sided polygon. Angle CAD is the interior angle at vertex A of a regular 10-sided polygon.
A line through A is a line of symmetry of both polygons, with B and C on one side and D and E on the other (in the order B, C, ..., D, E around A).
Work out angle BAC.
Question 64 marksGrade 8-9
Three regular polygons meet at a point, with no gaps or overlaps.
Two of the polygons are regular pentagons.
Find the number of sides of the third polygon. You must show your working.