Important for :

1

B

Check through the options, each interior angle= | ( | 180° – | 360° | ) |

n |

If measure of each angle = 105°, then

180° – | 360° | = 105° |

n |

180° × n – 360° = 105° × n

75° × n = 360°

n = | 24 | |

5 |

which is impossible

Hence, option B is correct.

2

D

Let the number of sides of a polygon be n. Then,Sum of interior angles = (2n – 4) × 90°

Sum of exterior angles = 360°

∴ (2n – 4) × 90° = 2 × 360°

2n – 4 = 8

2n = 12

n = 6

Hence, option D is correct.

3

C

Let the number of sides of two regular polygons be x and 2x respectively. Then,( | 180° – | 360° | ) |
: |
( | 180° – | 360° | ) | = 2 : 3 |

x | 2x |

180° (x – 2) | × | x | = | 2 |

x | 180° (x – 1) | 3 |

3x – 6 = 2x – 2

x = 4

∴ Number of sides = x = 4 and 2x = 2 × 4 = 8

Hence, option C is correct.

4

C

360° | – | 360° | = 6° |

n – 1 | n + 2 |

360° | ( | n + 2 – n + 1 | ) | = 6° |

(n – 1) (n + 2) |

(n – 1) (n + 2) = 180

n

n

n

n(n + 14) – 13(n + 14) = 0

(n – 13) (n + 14) = 0

n = 13, – 14 [

Hence, optino C is correct.

5

D

Let the number of sides of a regular polygon be n. Then,180° – | 360° | = 150° |

n |

180° × n – 360° = 150° × n

30° × n = 360°

n = 12

Hence, option D is correct.