The simple closed curves which are made up of line segments only are called the **Polygons**.

**Classification of Polygons**

Polygons can be classified by the **number of sides or vertices** they have.

Number of sides | Name of Polygon | Figure |

3 | Triangle | |

4 | Quadrilateral | |

5 | Pentagon | |

6 | Hexagon | |

7 | Heptagon | |

8 | Octagon | |

9 | Nonagon | |

10 | Decagon | |

n | n-gon |

**Diagonals**

Any line segment which connects the two non-consecutive vertices of a polygon is called **Diagonal**.

**Convex and Concave Polygons**

The polygons which have all the diagonals inside the figure are known as **a Convex Polygon**.

The polygons which have some of its diagonals outside the figure also are known as a **Concave Polygon**.

**Regular and Irregular Polygons**

Polygons which are equiangular and equilateral are called **Regular Polygons** i.e. a polygon is regular if –

- It’s all sides are equal.
- It’s all angles are equal.

square is a regular polygon but a rectangle is not as its angles are equal but sides are not equal.

**Angle Sum Property**

The sum of all the interior angles of a polygon remains the same according to the number of sides regardless of the shape of the polygon.

The sum of interior angles of a polygon is-

**(n – 2) × 180°**

Where n = number of sides of the polygon

**Example**

Polygon | Number of Sides | Sum of Interior Angles |

Triangle | 3 | (3 – 2) × 180° = 180° |

Quadrilateral | 4 | (4 – 2) × 180° = 360° |

n-gon | n | (n – 2) × 180° |

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