## Angle sum in a polygon

If we know that the angles in a triangle add up to 180°, we can use this fact to work out the total angle sum inside any polygon. This is sometimes called the
interior angle sum (interior is just another word for inside - think interior designer!). If we pick a corner on a polygon and join that corner to each other corner, we form triangles inside. Each triangle has an angle sum of 180°. For example, in a pentagon, we form three triangles. Each has an angle sum of 180°, so the total angle sum inside a pentagon must be 180° x 3 = 540°. The angle sums of polygons are as follows: Triangle = 180° Quadrilateral = 360° Pentagon = 540° Hexagon = 720° Heptagon = 900° Octagon = 1080° The number of triangles is always two less than the number of sides. We can use this to write a general formula linking the number of sides to the interior angle sum: Interior angle sum = (n - 2) x 180. |

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## External links

- BBC Bitesize: Notes on angle sums of polygons, with a couple of problems to try.
- Mymaths: Lesson on angle sums of polygons. Test yourself with the online homework.
- IXL: Test yourself with this online worksheet. It has full solutions for incorrect answers so you can find out where you have gone wrong.