MA25-07 Maths Coming soon
Exterior angles and regular polygons
This lesson is coming soon.
In this lesson
Use the fact that the exterior angles of any polygon sum to 360 degrees, calculate the interior and exterior angle of a regular polygon, and correctly relate the two angles at the same vertex without swapping them.
What it covers
- The exterior angles of any convex polygon always sum to 360 degrees, whatever the shape
- Exterior angle of a REGULAR polygon = 360 / number of sides, and using it to find the number of sides from a given exterior angle
- Interior angle of a regular polygon = 180 - exterior angle, and correctly converting between interior and exterior at the same vertex without swapping them
- Using the number of sides to find interior/exterior angles of a regular polygon, and vice versa
Key words
For: Edexcel IGCSE 4MA1, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, Cambridge IGCSE 0580, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| Edexcel IGCSE 4MA1 | F4.2B | Understand and use the term 'quadrilateral' and the angle sum property of quadrilaterals |
| Edexcel IGCSE 4MA1 | F4.2D | Understand the term 'regular polygon' and calculate interior and exterior angles of regular polygons |
| Edexcel IGCSE 4MA1 | F4.2E | Understand and use the angle sum of polygons |
| AQA GCSE 8300 | G3 | Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles |
| Edexcel GCSE 1MA1 | G3 | Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons) |
| Eduqas GCSE C300 | FG3 | Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons) |
| Eduqas GCSE C300 | HG3 | Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons) |
| Cambridge IGCSE 0580 | C4.6 | Angles |
| Cambridge IGCSE 0580 | E4.6 | Angles |
| OCR GCSE J560 | 8.03d | Derive and use the sum of the interior angles of a triangle is 180°. Derive and use the sum of the exterior angles of a polygon is 360°. Find the sum of the interior angles of a polygon. Find the interior angle of a regular polygon. |
For teachers
This GCSE Maths lesson teaches exterior angles and regular polygons. By the end, students should be able to use the fact that the exterior angles of any polygon sum to 360 degrees, calculate the interior and exterior angle of a regular polygon, and correctly relate the two angles at the same vertex without swapping them. It works through two worked examples and the mistakes examiners report.