Interior angles of a polygon formula: (n − 2) × 180°
The interior angles of a polygon formula is sum of interior angles = (n − 2) × 180°.
What each letter means
- \(n\) the number of sides
When to use it
To find the angle sum of any polygon, or each interior angle of a regular polygon: (n − 2) × 180° ÷ n.
Worked examples
1. Find the size of each interior angle of a regular 12-sided polygon.
- Sum \(=(12-2)\times180^\circ=1800^\circ\)
- Each angle \(=1800^\circ\div12\)
Answer: \(150^\circ\)
2. Each exterior angle of a regular polygon is \(24^\circ\). How many sides does it have?
- \(n=360^\circ\div24^\circ\)
Answer: 15 sides
Common mistake
Using n × 180°. A polygon with n sides splits into n − 2 triangles from one vertex.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | Not given: learn it |
| Cambridge 0580 | Not given: learn it |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
- Practise 4MA1 angles and polygons questions
- Practise 0580 angles questions
- Revise Geometry and trigonometry notes
- Print Edexcel 4MA1 (Higher) one-page formula sheet
Questions
What is the interior angles of a polygon formula?
The interior angles of a polygon formula is sum of interior angles = (n − 2) × 180°. n: the number of sides.
Is the interior angles of a polygon given in the exam?
Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: not given: learn it. This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
What do the exterior angles of a polygon add up to?
360°, for any convex polygon. Each exterior angle of a regular polygon is 360° ÷ n.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.