EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
📏
Geometry & Measures · Foundation & Higher

Properties of polygons

A polygon is a closed 2D shape with straight sides. You need to know the properties of regular and irregular polygons, including angle sums and names.

Revising properties of polygons the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Properties of polygons GCSE” on the site for the complete guide.

🔑

Key facts to remember

  • 1Interior angle sum of a polygon with n sides = (n − 2) × 180°.
  • 2Each interior angle of a regular polygon = (n − 2) × 180° ÷ n.
  • 3Each exterior angle of a regular polygon = 360° ÷ n.
  • 4Interior + exterior angle = 180° (angles on a straight line).
  • 5The sum of all exterior angles of any polygon = 360°.
  • 6Regular polygons have all sides equal and all angles equal.
📐

Formulas

Interior angle sum
(n − 2) × 180°

n = number of sides

Each interior angle (regular)
(n − 2) × 180° ÷ n
Each exterior angle (regular)
360° ÷ n
✍️

Worked examples

Example 1

Find the interior angle of a regular hexagon.

Working

  1. n = 6
  2. Interior angle sum = (6 − 2) × 180° = 4 × 180° = 720°
  3. Each interior angle = 720° ÷ 6 = 120°
Answer120°
Example 2

A regular polygon has exterior angles of 24°. How many sides does it have?

Working

  1. Number of sides = 360° ÷ exterior angle
  2. n = 360° ÷ 24° = 15
Answer15 sides
⚠️

Common mistakes

✗Using the interior angle sum formula for just one interior angle without dividing by n.
✗Confusing interior and exterior angles.
✗Forgetting that the exterior angle formula (360 ÷ n) only works for regular polygons.
🎯

Exam tips

✓Learn the formula (n − 2) × 180° — it works for all polygons, regular or irregular.
✓For exterior angles: they always sum to 360° regardless of the number of sides.

Ready to test yourself on Properties of polygons?

Get AI-marked practice questions on exactly this subtopic.

Practice this topic →
← All topicsDashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

▶interior exterior angles polygons GCSE▶regular polygon angles GCSE maths▶angle sum polygon GCSE▶properties of polygons GCSE maths

Opens YouTube — pick any free GCSE video.