Polygons
A closed shape with many sides is a polygon.
Sum of Interior Angles
If the number of sides is n and the sum of interior angles is T,
T = (n-2)180
The table, given below, shows how the sum of interior angles varies with the number of sides.
Sum of Exterior Angles
The sum of exterior angles is 3600, regardless of the number of sides.
| Polygon | No of Sides | Sum of Interior Angles |
|---|---|---|
| Triangle | 3 | 1800 |
| Square | 4 | 3600 |
| Pentagon | 5 | 5400 |
| Hexagon | 6 | 7200 |
| Heptagon | 7 | 9000 |
| Octagon | 8 | 10800 |
| Nonagon | 9 | 12600 |
| Decagon | 10 | 14400 |
You can practise how the number of sides is related to the sum of interior angles - and exterior angles too - with the following simulation.
Please note that the polygons created are regular - sides of equal length.
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