This key facts covers Common Polygon Angles within Angles in Polygons for GCSE Mathematics. Revise Angles in Polygons in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 3 of 10 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Common Polygon Angles
| Polygon | Sides (n) | Interior Sum | Each Interior (regular) | Each Exterior (regular) |
|---|---|---|---|---|
| Triangle | 3 | 180° | 60° | 120° |
| Quadrilateral | 4 | 360° | 90° | 90° |
| Pentagon | 5 | 540° | 108° | 72° |
| Hexagon | 6 | 720° | 120° | 60° |
| Octagon | 8 | 1080° | 135° | 45° |
| Decagon | 10 | 1440° | 144° | 36° |
Practice questions for Angles in Polygons
What is the sum of the interior angles of a hexagon?
Explain how the formula (n − 2) × 180° for the sum of interior angles of a polygon is derived.
Quick recall flashcards
Interior Angle Sum
Sum = (n - 2) × 180° for n-sided polygon
Exterior Angle Sum
Always 360° for any polygon