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Q n P Level 1
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Q n P Quiz 4
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Q n P Quiz 1
Directions: Study the following questions and choose the right answer:
important for :
CDSE
CGL Tier 2
CGLTier 1
SSC 10+2
1.
Measure of each interior angle of a regular polygon can never be :
A.
150°
B.
105°
C.
108°
D.
144°
Ans
B
Explain it
Answer:
Option
B
Explanation:
Check through the options, each interior angle
=
(
180° –
360°
)
n
If measure of each angle = 105°, then
180° –
360°
= 105°
n
180° × n – 360° = 105° × n
75° × n = 360°
n =
24
5
which is impossible
Hence, option B is correct.
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2.
The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is
A.
10
B.
8
C.
12
D.
6
Ans
D
Explain it
Answer:
Option
D
Explanation:
Let the number of sides of a polygon be n. Then,
Sum of interior angles = (2n – 4) × 90°
Sum of exterior angles = 360°
∴ (2n – 4) × 90° = 2 × 360°
2n – 4 = 8
2n = 12
n = 6
Hence, option D is correct.
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3.
The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively
A.
6, 12
B.
5, 10
C.
4, 8
D.
7, 14
Ans
C
Explain it
Answer:
Option
C
Explanation:
Let the number of sides of two regular polygons be x and 2x respectively. Then,
(
180° –
360°
)
:
(
180° –
360°
)
= 2 : 3
x
2x
180° (x – 2)
×
x
=
2
x
180° (x – 1)
3
3x – 6 = 2x – 2
x = 4
∴ Number of sides = x = 4 and 2x = 2 × 4 = 8
Hence, option C is correct.
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4.
There are two regular polygons with number of sides equal to (n – 1) and (n + 2). Their exterior angles differ by 6°. The value of n is
A.
14
B.
12
C.
13
D.
11
Ans
C
Explain it
Answer:
Option
C
Explanation:
360°
–
360°
= 6°
n – 1
n + 2
360°
(
n + 2 – n + 1
)
= 6°
(n – 1) (n + 2)
(n – 1) (n + 2) = 180
n
^{2}
+ n – 2 = 180
n
^{2}
+ n – 182 = 0
n
^{2}
+ 14n – 13n – 182 = 0
n(n + 14) – 13(n + 14) = 0
(n – 13) (n + 14) = 0
n = 13, – 14 [
∵
n ≠ – 14 ]
Hence, optino C is correct.
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5.
If each interior angle of a regular polygon is 150°, the number of sides of the polygon is
A.
8
B.
10
C.
15
D.
None of these
Ans
D
Explain it
Answer:
Option
D
Explanation:
Let the number of sides of a regular polygon be n. Then,
180° –
360°
= 150°
n
180° × n – 360° = 150° × n
30° × n = 360°
n = 12
Hence, option D is correct.
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