Deriving the sum of interior angles in multiple ways

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

Exterior angles of polygons

Interior and exterior angles of regular 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 time the number of sides of a polygon increases by 1, the sum of the interior angles increases by {{}}°.

The interior angles in 19-sided polygon sum to 3060°. Therefore the interior angles in a 20-sided polygon sum to {{}}°.

Which expression can be used to calculate the sum of interior angles in a polygon by substituting $$n$$ for the number of sides?

A triacontagon is a polygon with 30 sides. Which calculation finds the sum of its interior angles?

A tetracontagon is a polygon with 40 sides. Its interior angles sum to {{}}°.

A polygon has interior angles which sum to 720°. The polygon has {{ }} sides.

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

A hendecagon has 11 sides. The minimum number of triangles that it could be split into is {{ }}.

A hexadecagon has 16 sides. Which calculation would find the sum of its interior angles?

Evaluate the expression $$20(x − 2)$$ when $$x=5$$.

Starter Quiz

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