7.1 Polygon Angle Sums

Notes

A polygon is a closed figure made of segments. A regular polygon has all sides and all angles congruent.

• Interior angle sum of an $n$-gon: $(n - 2) \cdot 180^\circ$.
• Each interior angle of a regular $n$-gon: $\displaystyle \frac{(n - 2) \cdot 180^\circ}{n}$.
• Exterior angle sum of any convex polygon, one at each vertex: $360^\circ$. Each exterior angle of a regular $n$-gon: $\displaystyle \frac{360^\circ}{n}$.
• Example: a hexagon's angles add to $4 \cdot 180 = 720^\circ$; each angle of a regular hexagon is $120^\circ$.