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 \(360^{\circ}\). The pentagon below can be divided into three triangles giving \(540^{\circ}\) 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) | \(60^{\circ}\) |

\(4\) (square) | \(90^{\circ}\) |

\(5\) (pentagon) | \(108^{\circ}\) |

\(6\) (hexagon) | \(120^{\circ}\) |

\(7\) (heptagon) | \(129^{\circ}\) |

\(8\) (octagon) | \(135^{\circ}\) |

\(\infty\) (infinite} | \(180^{\circ}\) |

The table shows that as the number of sides of a regular polygon is increased to infinity, the polygon angle approaches \(180^{\circ}\), 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 \(360^{\circ}\), only those regular polygons whose angle can be divided evenly into \(360^{\circ}\) will tessellate. As the table shows, the triangle, square, and hexagon are the only regular polygons that can be made into a tessellate.