Polygons summary

Key learning points

• Interior sum of an $n$-gon: $(n-2)\times180^\circ$.
• Regular polygon: each exterior $=360^\circ/n$; interior $=180^\circ-$ exterior.
• Tessellation links to angles at a point.

Worked example 1 — Interior sum

Sum of interior angles of a hexagon?

Working

$(n-2)\times180^\circ$.

Worked example 2 — Regular hexagon

Each interior angle of a regular hexagon?

Working

Exteriors sum to $360^\circ$.

Worked example 3 — Exterior angle

Regular polygon, exterior $24^\circ$. Number of sides?

Working

$n=360^\circ/\text{exterior}$.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.