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Hi
Directions: Study the following questions and choose the right answer:
Important for :
CDSE
CGL Tier 2
CGLTier 1
Railways
SSC 10+2
1
Measure of each interior angle of a regular polygon can never be :
A
150°
B
105°
C
108°
D
144°
» Explain it
Correct Option:
B
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.
1
A
B
C
D
» Explain it
सही विकल्प :
B
B
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
» Explain it
Correct Option:
D
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.
2
A
B
C
D
» Explain it
सही विकल्प :
D
D
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
» Explain it
Correct Option:
C
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.
3
A
B
C
D
» Explain it
सही विकल्प :
C
C
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
» Explain it
Correct Option:
C
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.
4
A
B
C
D
» Explain it
सही विकल्प :
C
C
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
» Explain it
Correct Option:
D
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.
5
A
B
C
D
» Explain it
सही विकल्प :
D
D
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