This key facts covers Essential Formulas 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 2 of 10 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Essential Formulas
| What You Want | Formula | Notes |
|---|---|---|
| Sum of interior angles | (n − 2) × 180° | n = number of sides |
| One interior angle (regular) | (n − 2) × 180° ÷ n | All angles equal in regular polygon |
| Sum of exterior angles | Always 360° | Works for ANY polygon! |
| One exterior angle (regular) | 360° ÷ n | Quickest method for regular polygons |
| Interior + Exterior | = 180° | They're on a straight line |
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
Exterior Angle Sum
Always 360° for any polygon
Interior Angle Sum
Sum = (n - 2) × 180° for n-sided polygon