Polygons

Description

A polygon is a closed 2D shape with straight sides. Polygons are named by their number of sides.

Common polygons: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10).

Interior angles: $$\text{Sum of interior angles} = (n - 2) \times 180°$$ where $n$ is the number of sides.

$$\text{Each interior angle of a regular polygon} = \frac{(n-2) \times 180°}{n}$$

Exterior angles: the exterior angles of any polygon sum to $360°$. $$\text{Each exterior angle of a regular polygon} = \frac{360°}{n}$$

Example: For a regular hexagon ($n = 6$): $$\text{Interior angle} = \frac{4 \times 180°}{6} = 120°, \quad \text{Exterior angle} = \frac{360°}{6} = 60°$$

Note: interior angle + exterior angle = 180° (they are supplementary).

Common error: using $n \times 180°$ instead of $(n-2) \times 180°$ for the angle sum.

Links

Angle facts