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A Polygon is a plane figure formed by at least three sides and angles. The table below displays details of some of the common polygons.

Name |
No. of sides |
No. of angles |

Triangle | 3 | 3 |

Quadrilaterals | 4 | 4 |

Pentagon | 5 | 5 |

Hexagon | 6 | 6 |

Heptagon | 7 | 7 |

Octagon | 8 | 8 |

Nonagon | 9 | 9 |

Decagon | 10 | 10 |

n-gon | n | n |

**Polygon Angles: **Angles of a polygon are represented in two ways.

**Interior Angles**: An interior angle of a polygon is an angle formed inside the polygon by any two adjacent sides of the polygon. The sum of the interior angles of a polygon is based on the number of sides the polygon has, and it is calculated as

Sum of interior angles = (n-2) * 180^{o}

“n” is the number of sides of a polygon

Example 1: Calculate the sum of interior angles of a pentagon.

Solution: Pentagon has 5 sides (n =5)

Sum of interior angles = (5-2) * 180^{o}

= 3 * 180^{o}

= 540^{o}

**Exterior angles:** Angles formed between any side and extension of its adjacent side. The sum of exterior angles of a polygon is equal to 360^{o }. The ^{ }Figure below represents the exterior angles of a pentagon.

Fig 1: Exterior angles of a pentagon

Measure of angle A+B+C+D+E= 360^{o}

Based on the length of the sides and size of the angles, polygons are classified as Regular and Irregular polygons.

**Regular polygon**: Each side of a polygon is equal in length, and each angle is equal in size.

Fig 2: Regular pentagon

Each angle of a regular polygon = Sum of angles of polygon/Number of sides of a polygon

Example 2: What is the measure of each interior angle of a regular octagon?

Solution: Octagon has 8 sides (n =8)

Sum of interior angles= (8 – 2) * 180^{o}

= 6 * 180^{o}

= 1080^{o}

Each angle of a regular Octagon = 1080^{o}/8

= 135^{o}

**Number of sides of a polygon:** Let’s say each exterior angle of a regular polygon is *x*^{o} , the number of sides of a polygon is calculated as

Number of sides = Sum of exterior angles/*x*^{o}

Example 3: The measure of one of the exterior angles of a polygon is 20^{o} . Number of sides of a polygon is?

Solution: Number of sides = Sum of exterior angles/20^{o}

= 360^{o}/ 20^{o}

= 18

Therefore, the given polygon has 18 sides.

**Irregular polygon**: Each side and angle of a polygon is unequal in length and size. Example

Fig 3: irregular pentagon