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  • These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
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Geometry and Mensuration: Test 27

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Question 1
Each internal angle of regular polygon is two times its external angle. Then the number of sides of the polygon is:
A
8
B
6
C
5
D
7
Question 1 Explanation: 
The interior angle + exterior angle =180o
Thus the interior angle = 120o and each exterior angle  = 60o
The sum of all the exterior angles = 3600
The number of sides = 3600/600 = 6
Correct option is (b)
Question 2
Ratio of the number of sides of two regular polygons is 5: 6 and the ratio of their each interior angle is 24: 25. Then the number of sides of these tow polygons are
A
20, 24
B
15, 18
C
10, 12
D
5, 6
Question 2 Explanation: 
image-13
Question 3
Measure of each interior angle of a regular polygon can never be;
A
150o
B
105o
C
108o
D
144o
Question 3 Explanation: 
image-10
Question 4
ABCD is a cyclic quadrilateral and O is the center of the circle. If ∠COD= 140o and ∠BAC= 40o, then the value of ∠BCD is equal to
A
70o
B
90o
C
60o
D
80o
Question 4 Explanation: 
image-11
∠COD=140, thus∠ CAD= ½ of ∠COD= 70.
∠BAD= 40+70=110.
∠BCD= 180-110=70.
Correct option is (a)
Question 5
ABCD is a cyclic trapezium with AB||DC and AB= diameter of the circle. If ∠CAB= 30o, then ∠ADC is
A
60o
B
120o
C
150o
D
30o
Question 5 Explanation: 
image-12
Here ∠CAB = 300 and ∠ACB = 900 Hence ∠ABC = 600
Now ∠ADC + ∠ABC = 1800
∠ADC = 1800 - 600 = 1200
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