Sum

**Fill in the blanks:**

In case of regular polygon, with

Number of sides |
Each exterior angle |
Each interior angle |

(i) 6 | _________ | __________ |

(ii) 8 | _________ | __________ |

(iii) ________ | 36° | __________ |

(iv) _______ | 20° | __________ |

(v) _________ | _________ | 135° |

(vi) ________ | _________ | 165° |

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#### Solution

Number of sides |
Each exterior angle |
Each interior angle |

(i) 6 | 60° |
120° |

(ii) 8 | 45° |
135° |

(iii) 10 |
36° | 144° |

(iv) 18 |
20° | 160° |

(v) 8 |
45° |
135° |

(vi) 24 |
15° |
165° |

(i) Each exterior angle = `360^circ/6 = 60^circ`

Each interior angle = 180° - 60° = 120°

(ii) Each exterior angle = `(360°)/8` = 45°

Each interior angle = 180° - 45° = 135°

(iii) Since each exterior angles = 36°

∴ Number of sides = `(360°)/(36°) = 10`

Also, interior angle = 180°- 20° = 160°

(iv) Since each exterior angles = 20°

∴ Number of sides = `(360°)/(20°) = 18`

Also, interior angle = 180° - 20° = 160°

(v) Since interior angles = 135°

∴ exterior angle = 180° - 135°

∴ Number of sides = `(360°)/(45°) = 8`

(vi) Since interior angle = 165°

∴ exterior angle = 180° - 165° = 15°

∴ Number of sides = `(360°)/(15°) = 24`

Concept: Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal

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