Geometry · Quick Reference

Polygons Cheat Sheet

Geometry · Lesson 8/16

In one line: a polygon is any closed shape made entirely of straight line segments — from simple triangles to complex many-sided figures, they're everywhere in geometry.

Key Ideas

1Polygon. A closed, two-dimensional shape made up of straight sides, with no curves and no gaps.

2Naming Polygons by Sides. Triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), and so on.

3Regular Polygons. A polygon where all sides are equal length and all interior angles are equal.

4Sum of Interior Angles. For any polygon with n sides, the interior angles sum to (n-2)*180°.

5Sum of Exterior Angles. The exterior angles of any convex polygon always sum to exactly 360°, regardless of how many sides it has.

Worked Examples

Find the sum of interior angles of a hexagon (6 sides).

720°

Find each interior angle of a regular pentagon (5 sides).

108° per angle

A polygon has interior angles summing to 1080°. How many sides does it have?

8 sides (an octagon)

Formulas

Sum of interior angles = (n-2)*180°

Each interior angle of a regular polygon = [(n-2)*180°] / n

Practice Yourself

Find the sum of interior angles of a quadrilateral (4 sides).

360°

Find the sum of interior angles of an octagon (8 sides).

1080°

Find each interior angle of a regular hexagon.

120°