Geometry and Mensuration: Test 27

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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 =180^o
Thus the interior angle = 120^o and each exterior angle  = 60^o
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: 

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: 

Question 4

ABCD is a cyclic quadrilateral and O is the center of the circle. If ∠COD= 140^o and ∠BAC= 40^o, then the value of ∠BCD is equal to

A	70o
B	90o
C	60o
D	80o

Question 4 Explanation: 

∠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= 30^o, then ∠ADC is

A	60o
B	120o
C	150o
D	30o

Question 5 Explanation: 

Here ∠CAB = 30⁰ and ∠ACB = 90⁰ Hence ∠ABC = 60⁰
Now ∠ADC + ∠ABC = 180⁰
∠ADC = 180⁰ - 60⁰ = 120⁰

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