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## Geometry and Mensuration: Test 26

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Question 1 |

The number of sides in two regular polygons are in the ratio 5: 4 and the difference between each interior angle of the polygons is 3o. Then the number of sides is

15, 12 | |

30, 24 | |

10, 8 | |

21, 16 |

Question 1 Explanation:

$\displaystyle \begin{array}{l}Let\text{ }the\text{ }number\text{ }of\text{ }sides\text{ }be\text{ }5xand\text{ }4xrespectively\\\frac{\left( 2\times 5x-4 \right){{90}^{o}}}{5x}-\frac{\left( 2\times 4x-4 \right)\times {{90}^{o}}}{4x}={{3}^{{}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ \begin{array}{l}each\,\,\,\,\operatorname{int}erior\,\,angle\,\\=\left( \frac{2n-4}{n} \right)\times {{90}^{o}}\end{array} \right]\\\Rightarrow \left( 10x-4 \right)\times {{360}^{o}}-\left( 8x-4 \right)\times {{450}^{o}}=20x\times {{3}^{o}}\\\Rightarrow 120x-48-120x+60=2x\\\Rightarrow 2x=12\Rightarrow x=6\\Therefore\,\,\,Number\,\,of\,\,\,sides\\=30\,\,and\,\,24\end{array}$

Question 2 |

ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If âˆ ABC= 72

^{o}, then the measure of the BCD is162 ^{o} | |

18 ^{o} | |

108 ^{o} | |

72 ^{o} |

Question 3 |

If an exterior angle of a cyclic quadrilateral be 50

^{o}, then the interior opposite angle is:130 ^{o} | |

40 ^{o} | |

50 ^{o} | |

90 ^{o} |

Question 3 Explanation:

The immediate internal angle = 180

The opposite internal angle = 180

Correct option is (c).

^{0}-50^{0 }= 130^{0}The opposite internal angle = 180

^{0 }- 130^{0}= 50^{0}.Correct option is (c).

Question 4 |

The ratio of the length of the parallel sides of a trapezium is 3: 2. The shortest distance between them is 15cm. If the area of the trapezium is 450 cm

^{2}, the sum of the lengths of the parallel sides is15 cm | |

36 cm | |

42 cm | |

60 cm |

Question 4 Explanation:

$ \begin{array}{l}\frac{1}{2}\times 15\times (\text{Sum of the length of two parallel sides})=450\\\text{Sum of length of parallel sides = 60}\text{.}\end{array}$

Question 5 |

If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is

9âˆš3cm | |

6âˆš3cm | |

3âˆš3cm | |

6 cm |

Question 5 Explanation:

$ \begin{array}{l}Let\text{ }the\text{ }side\text{ }of\text{ }equilateral\text{ }triangle\text{ }be\text{ }x.\\\frac{1}{3}.\frac{\sqrt{3}}{2}x=3\\=>x=6\sqrt{3}\end{array}$

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