MA25-06 Maths Coming soon
Interior angles of polygons
This lesson is coming soon.
In this lesson
Derive the formula for the sum of interior angles of a polygon, (n-2) x 180 degrees, by splitting it into triangles, and use it to find a missing interior angle, the number of sides, or the quadrilateral 360-degree special case.
What it covers
- Splitting a polygon into (n-2) triangles by drawing every diagonal from one single vertex, to derive the interior angle sum formula (n-2) x 180 degrees
- Using the formula to find a missing interior angle in an irregular polygon
- Using the formula to find the number of sides given the total interior angle sum
- The quadrilateral 360-degree angle sum as the n=4 special case of the same general formula
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 interior angles of polygons. By the end, students should be able to derive the formula for the sum of interior angles of a polygon, (n-2) x 180 degrees, by splitting it into triangles, and use it to find a missing interior angle, the number of sides, or the quadrilateral 360-degree special case. It works through two worked examples and the mistakes examiners report.