Polygons & Angles

Explore how the number of sides controls interior and exterior angles, then practise applying the rules.

Curriculum rangeYears 7–11

sides6

Green = interior angle Pink = exterior angle

Interior angle sum

(n-2) \times 180° = 720°

Each interior angle

720° \div 6 = 120°

Exterior angle sum

360°

Each exterior angle

360° \div 6 = 60°

The interior angle sum formula works for any polygon with this many sides -- dividing by n to get "each angle" only works when the polygon is regular (all sides and angles equal).

Learning notes

Polygons & Angles essentials

Keep these rules beside you while you explore and practise.

1Interior angle sum

Split an n-sided polygon into n − 2 triangles.

S=(n-2)\times180^\circ

2Regular interior angles

For a regular polygon, all interior angles are equal.

\text{Each interior angle}=\dfrac{(n-2)\times180^\circ}{n}

3Exterior angles

The exterior angles of any polygon add to 360°.

\text{Regular exterior angle}=\dfrac{360^\circ}{n}

4Find the number of sides

n=\dfrac{360^\circ}{\text{exterior angle}}

💡Check: an interior angle and its adjacent exterior angle add to 180°.