Determining the number of degrees in the angles of other polygons can be calculated by dividing the polygon into triangles. A quadrangle (four sides) can be divided into two triangles so that the total of its angles is 360∘. The pentagon below can be divided into three triangles giving 540∘ total degrees, etc.
It is interesting to see what happens when regular polygons (all angles equal) are divided into triangles and the number of degrees in each angle is calculated:
| Number of Sides | Degrees in Each Angle |
|---|---|
| 3 (triangle) | 60∘ |
| 4 (square) | 90∘ |
| 5 (pentagon) | 108∘ |
| 6 (hexagon) | 120∘ |
| 7 (heptagon) | 129∘ |
| 8 (octagon) | 135∘ |
| ∞ (infinite} | 180∘ |
The table shows that as the number of sides of a regular polygon is increased to infinity, the polygon angle approaches 180∘, or a straight line! This implies that a circle can be thought of as a polygon with an infinite number of infinitely short straight sides, a concept often used in calculus.
The above table can also be used to determine which regular polygons can be used to make a tessellate. Since the sum of the angles around a vertex point of a tessellation must be 360∘, only those regular polygons whose angle can be divided evenly into 360∘ will tessellate. As the table shows, the triangle, square, and hexagon are the only regular polygons that can be made into a tessellate.