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In a regular polygon, if an interior angle is equal to four times the exterior angle, then number of sides in the polygon is

A) 7
B) 8
C) 10
D) 11

Correct Answer:



C) 10

Description for Correct answer:
Interior angle (I) + Exterior angle (E) = \( \Large 180 ^{\circ} \)

Therefore, I + E = \( \Large 180 ^{\circ} \)

Now I = AE (given)

Therefore, AE + E = \( \Large 180 ^{\circ} \)

E = \( \Large 36 ^{\circ} \)

Therefore, number of sides = \( \Large \frac{360 ^{\circ} }{E} = \frac{360}{36} = 10 \)

Part of solved Quadrilateral and parallelogram questions and answers : >> Elementary Mathematics >> Quadrilateral and parallelogram

Comments

Similar Questions

1). If one side of a regular polygon with seven sides is produced, then exterior angle (in degrees) has the magnitude

A). 60

B). \( \Large 51\frac{3}{7} \)

C). 45

D). 40

2). The angle BDE in a regular hexagon ABCDEFFA is equal to

A). \( \Large 120 ^{\circ} \)

B). \( \Large 105 ^{\circ} \)

C). \( \Large 90 ^{\circ} \)

D). \( \Large 60 ^{\circ} \)

3). If in a parallelogram ABCD, bisectors of consecutive angles A and B intersect at P, then \( \Large \angle APB \) is equal to

A). \( \Large 30 ^{\circ} \)

B). \( \Large 45 ^{\circ} \)

C). \( \Large 60 ^{\circ} \)

D). \( \Large 90 ^{\circ} \)

4). The area of the shaded portion is

A). 8 sq. cm

B). 6 sq. cm

C). 16 sq. cm

D). 4 sq. cm

5). Match List-I with List-II and select the correct answer using the codes given below the lists List-I
A. Opposite sides equal and parallel
B. Opposite sides equal and one angle \( \Large 90 ^{\circ} \)
C. All sides equal and each angle \( \Large 90 ^{\circ} \)
D. All sides equal and diagonals at right angles
List-II
1. Rectangle
2. Square
3. Rhombus
4. Parallelogram
Codes:
A B C D

A). 4 1 3 2

B). 3 4 2 1

C). 4 1 2 3

D). 2 4 1 3

6). The area of a rectangle and a square are equal. The side of the square is 5 cm and smaller side of the rectangle is half that of the square. The length of other side of the rectangle would be

A). 5 cm

B). 8 cm

C). 10 cm

D). 12.5 cm

7). The perimeter of a square is 12 cm and that of another is 16 cm. The side of a square whose area is equal to sum of the areas of the above two squares would be

A). 4 cm

B). 5 cm

C). 5.5 cm

D). 6 cm

8). If perimeter of a rectangle is 48 metres and its area is \( \Large 135 m^{2} \), then sides of the rectangle are

A). 15 m, 9 m

B). 19 m, 5 m

C). 45 m, 3 m

D). 27 m, 5 m

9). The maximum number of tangents which can be drawn from an external point to a circle is

A). two

B). one

C). zero

D). none of these

10). A circular running track is 10 m wide. The difference in the length of the outer boundary and the inner boundary
I. depends on the length of the track
II. depends on the radius of the inner boundary
III. depends on the area of the track
IV is \( \Large 20 \pi m \).
Select the correct answer using the codes below:
Codes :

A). I, II and III

B). I and III

C). II and III

D). IV alone