Lesson 6.1: Angles of Polygons
Angles of Polygons
Interior Angle Sum
The sum of the interior angles of a convex Polygon with n sides is:
S = (n − 2) × 180°
| Polygon | Sides | Angle Sum |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
| n-gon | n | (n−2)×180° |
Each Interior Angle of a Regular Polygon
Each Angle = (n − 2) × 180° / n
Exterior Angle Sum
The sum of the exterior angles of any convex Polygon (one at each vertex) is always 360°, regardless of the number of sides.
Each exterior Angle of a regular Polygon = 360° / n.