GCSE & IGCSE maths practice

Angles in polygons questions and answers

The interior angles of a polygon with $n$ sides add up to $(n - 2) \times 180°$ . The exterior angles of any polygon add up to $360°$ , so each exterior angle of a regular polygon is $360° \div n$ . Interior and exterior angles at a vertex add up to $180°$ .

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Angles in polygons guide

Where angles in polygons comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: deduce and use the angle sum in any polygon, and derive properties of regular polygons.
Cambridge IGCSE (0580)	Core and Extended: interior and exterior angles and the angle sum of polygons, and the angle properties of regular polygons.

The method

Interior angle sum = (n − 2) × 180°.
Regular polygon: exterior angle = 360° ÷ n; interior = 180° − exterior.
Number of sides = 360° ÷ exterior angle.
Missing angle: angle sum minus the angles you know.

Angles in polygons questions

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Warm-up

Question 1Warm-upFoundation

Find the sum of the interior angles of a pentagon.

Question 2Warm-upFoundation

Find the size of each exterior angle of a regular hexagon.

Exam-style

Question 3Exam-styleFoundation

Find the size of each interior angle of a regular octagon.

Question 4Exam-styleFoundation

Each exterior angle of a regular polygon is $24°$ . How many sides does it have?

Question 5Exam-styleFoundation

Find the sum of the interior angles of a decagon (10 sides).

Question 6Exam-styleFoundation

Each interior angle of a regular polygon is $160°$ . How many sides does it have?

Challenge

Question 7ChallengeFoundation

A pentagon has angles $100°$ , $120°$ , $95°$ , $110°$ and $x$ . Find $x$ .

Question 8ChallengeFoundation

Can a regular polygon have an interior angle of $130°$ ?

Common mistakes

Using n × 180° for the angle sum.
Dividing 360 by the interior angle instead of the exterior.
Using exterior-angle rules for an irregular polygon's individual angles.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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