Sum

Fill in the blanks :

In case of regular polygon, with :

No.of.sides |
Each exterior angle |
Each interior angle |

(i) ___8___ | _______ | ______ |

(ii) ___12____ | _______ | ______ |

(iii) _________ | _____72°_____ | ______ |

(iv) _________ | _____45°_____ | ______ |

(v) _________ | __________ | _____150°_____ |

(vi) ________ | __________ | ______140°____ |

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#### Solution

No.of. sides |
Each exterior angle |
Each interior angle |

(i) 8 | 45° | 135° |

(ii) 12 | 30° | 150° |

(iii) 5 | 72° | 108° |

(iv) 8 | 45° | 135° |

(v) 12 | 30° | 150° |

(vi) 9 | 40° | 140° |

**Explanation:**

(i) Each exterior angle = `360^circ/8 = 45^circ`

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

(ii) Each exterior angle = `360^circ/12 = 30^circ`

Each interior angle = 180° - 30° = 150°

(iii) Since each exterior = 72°

∴ Number of sides = `360^circ/72^circ = 5`

Also interior angle = 180° - 72° = 108°

(iv) Since each exterior = 45°

∴ Number of sides = `360^circ/45^circ = 8`

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

(v) Since interior angle = 150°

Exterior angle = 180° - 150° = 30°

∴ Number of sides = `360^circ/30^circ = 12`

(vi) Since interior angle = 140°

Exterior angle = 180° - 140° = 40°

∴ Number of sides = `360^circ/40^circ = 9`

Concept: Regular Polynomial

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