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## Geometry and Mensuration: Level 1 Test 5

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Question 1 |

An angle is equal to 1/3 of its supplement. Find its measure.

60 degrees | |

80 degrees | |

90 degrees | |

45 degrees |

Question 1 Explanation:

$ \displaystyle \begin{array}{l}\operatorname{Re}quired\,\,angle\,\,x=\frac{1}{3}\left( 180-x \right)\\4x=180\\x={{45}^{0}}\end{array}$

Question 2 |

In Î”ABC, âˆ BAC= 90 degrees and AB= 1/2BC. Then the measure of âˆ ACB is:

60 degrees | |

30 degrees | |

45 degrees | |

15 degrees |

Question 2 Explanation:

Question 3 |

How many sides a regular polygon has with its interior angle eight times its exterior angle?

16 | |

24 | |

18 | |

20 |

Question 3 Explanation:

Let the interior angle be x,

Thus, x= 8(180-x)

=> 9x= 8(180) => x = 160

The exterior angle = 20

The number of sides=360/20 = 18

Thus, x= 8(180-x)

=> 9x= 8(180) => x = 160

The exterior angle = 20

^{o}The number of sides=360/20 = 18

Question 4 |

In a quadrilateral ABCD, âˆ B= 90 degrees and AD

^{2}= AB^{2}+ BC^{2}+ CD^{2}, then âˆ ACD is equal to90 degrees | |

60 degrees | |

30 degrees | |

None of these |

Question 5 |

If the lengths of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is.

8 cm | |

6 cm | |

5 cm | |

4.8 cm |

Question 5 Explanation:

Now since BD = median AD= BC.

Now since 8

The Â triangle is a right angled triangle (right angle at B)

Thus BD = AD=BC=1/2 x 10 =5 cm

Now since 8

^{2}+6^{2}=10^{2}The Â triangle is a right angled triangle (right angle at B)

Thus BD = AD=BC=1/2 x 10 =5 cm

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