A polygon is a flat (2D), closed figure made up of straight line segments.

A regular polygon has sides that are equal and interior (inside) angles that are all equal.

An interior angle is an angle formed inside a polygon by two of its edges.

An exterior angle is an angle on the outside of a polygon between an extension of an edge and its adjacent edge.

Interior and exterior angles of regular polygons

Maths

Checking understanding of angles from KS2

Securing understanding of angles from KS2

Formalising understanding of triangles from KS2

Formal angle notation

Corresponding angles

Alternate angles

Co-interior angles

Angles on parallel lines traversed by a straight line

The sum of the interior angles of any triangle

Using the sum of the interior angles of a triangle

Interior angles of a polygon

Deriving the sum of interior angles in multiple ways

Exterior angles of polygons

Missing angles

Problem solving with polygons

This unit gives pupils the opportunity to explore polygons and begin to generalise their understanding of interior/exterior angles in regular polygons. In the future unit, pupils will use the geometrical properties of a rhombus to perform various constructions

In this unit, pupils learnt how to calculate with angles at a point and angles on a straight line. In this unit, pupils extend their knowledge about angles in lines

In this unit pupils will investigate internal and external angles of polygons and angles made with a transveral and parallel lines. Pupils will develop their ability to formally prove properties of polygons to generalise.

Geometrical properties: polygons

Each exterior angle in a regular hexagon is {{}}°.

Each interior angle in a regular pentagon is {{}}°.

Is it possible for a decagon to be regular if one of its exterior angles is 30°?

Is it possible for an octagon to be regular if one of its interior angles is 45°?

Which calculations can be used to find the size of the shaded angle?

A {{}} polygon has sides that are equal and interior (inside) angles that are all equal.

a regular hexagon with a side length of 3 cm

a regular decagon with a side length of 2 cm

a regular pentagon with a side length of 6 cm

a regular octagon with a side length of 5 cm

Starting with the smallest, sort the shapes in ascending order according to their perimeters.

Interior and exterior angles of regular polygons

Lesson outcome