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Geometry and Mensuration: Test 16

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Question 1
Each interior angle of a regular polygon is 144o. The number of sides of the polygon is
A
8
B
9
C
10
D
11
Question 1 Explanation: 
If the number of sides of the polygon be n, then
(n-2)180 = 144n
=> 180n-360 = 144n
=> 36 n = 360
=> n= 10.
Correct option is (c)
Question 2
ABCD is a cyclic parallelogram. The angle ∠B is equal to:
A
30o
B
60o
C
45o
D
90o
Question 2 Explanation: 
17
Since the opposite angles of a cyclic quadrilateral
add upto180 and also the opposite angles of a parallelogram are equal,
we can conclude that B = 90.
Correct option is (d)
Question 3
ABCD is a cyclic trapezium such that AD||BC, If ∠ABC= 70o, then the value of ∠BCD is:
A
60o
B
70o
C
40o
D
80o
Question 3 Explanation: 
18
Since a cyclic trapezium is always isosceles we can conclude that ∠ABC = ∠BCD.
Thus ∠BCD = 70.
Correct option is (b)
Question 4
The ratio of the angles ∠A and ∠B of a  rhombus ABCD is 4: 5, then the value of ∠C is:
A
50o
B
45o
C
80o
D
95o
Question 4 Explanation: 
∠ C= ∠A.
∠B+∠A = 180.
Since ∠A: ∠B = 4:5 , we can conclude that
∠B = 100 and ∠A= 80.
Thus ∠C = 80.
Question 5
ABCD is a rhombus whose side AB= 4cm and ABC= 120o, then the length of diagonal BD is equal to:
A
1 cm
B
2 cm
C
3 cm
D
4 cm
Question 5 Explanation: 
19
Since the diagonal is cutting the rhombus into two equal equilateral triangles,
the diagonal BD = 4cm.
$ \displaystyle \begin{array}{l}From\,\,\,\,\Delta BOC,\\\cos {{60}^{o}}\,\,=\frac{BO}{4}\\\Rightarrow \,BO=\frac{1}{2}\times 4\\=2\,\,cm\\\therefore \,\,BD=2\times 2=4\,\,cm\end{array}$
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