Angle Sum of Polygon

A polygon with \(n\) sides can be split into \(n - 2\) triangles from one vertex, so its interior angles add to \((n - 2) \times 180^\circ\). In NSW Year 8 maths this subtopic takes the angle sums of triangles and quadrilaterals from Stage 4 and extends them to any polygon, which looks ahead to Stage 5.

You will name polygons from the pentagon to the dodecagon, find the angle sum of shapes such as a decagon or a 24-gon, and find one interior angle of a regular polygon. You will also use the fact that the exterior angles add to \(360^\circ\), work backwards from an angle to the number of sides, find missing angles in irregular polygons, and decide which regular tiles can cover a floor without gaps. It is part of Year 8 Geometry.