Geometry and Mensuration: Test 16

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Geometry and Mensuration: Test 16

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Question 1

Each interior angle of a regular polygon is 144^o. 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	30^o
B	60^o
C	45^o
D	90^o

Question 2 Explanation:

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= 70^o, then the value of ∠BCD is:

A	60^o
B	70^o
C	40^o
D	80^o

Question 3 Explanation:

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	50^o
B	45^o
C	80^o
D	95^o

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= 120^o, then the length of diagonal BD is equal to:

A	1 cm
B	2 cm
C	3 cm
D	4 cm

Question 5 Explanation:

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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