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## Geometry and Mensuration: Test 16

Congratulations - you have completed Geometry and Mensuration: Test 16. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 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: 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: 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: 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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