Polygon Angle Sums

Interior Angle Sum

For a polygon with $n$ sides: $\text{Sum of interior angles} = (n - 2) \times 180°$

Examples:

• Triangle ($n = 3$): $(3 - 2) \times 180° = 180°$
• Quadrilateral ($n = 4$): $(4 - 2) \times 180° = 360°$
• Pentagon ($n = 5$): $(5 - 2) \times 180° = 540°$
• Hexagon ($n = 6$): $(6 - 2) \times 180° = 720°$

Regular Polygon

A polygon with all sides congruent and all angles congruent.

Measure of each interior angle: $\frac{(n - 2) \times 180°}{n}$

Exterior Angle Sum

The sum of exterior angles (one at each vertex) of ANY polygon is always $360°$.

$\text{Sum of exterior angles} = 360°$

Regular Polygon Exterior Angle

For a regular polygon: $\text{Each exterior angle} = \frac{360°}{n}$

Finding Number of Sides

If you know the interior angle measure of a regular polygon: $n = \frac{360°}{180° - \text{interior angle}}$