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Q.

Statement (A) : If the interior angle of a regular polygon is 60°, then it has 3sides.

Statement (B) : If the interior and exterior angles of a regular polygon are equal, then it is a pentagon

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a

Both A and B are true

b

Both A and B are false

c

A is true and B is false

d

A is false and B is true

answer is C.

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Detailed Solution

I) The interior angle of a regular polygon is (n2)×180°n      (n is number of sides of regular polygon )

(n2)×180°n=60°

(n2)×1803=601n

(n2)×3=n

3n6=n

3nn=6

2n=6

n=3

 The number of sides of a regular polygon is 3.

II) The interior and exterior angles of a regular polygon are equal.

(n2)×180n=360n 

(n2)×1801n=3602n

n2=2

n=2+2

n=4

The number of sides of a regular polygon = 4.

If the interior and exterior angles of a regular polygon are equal, then regular polygon  is a quadrilateral.

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