Question

if in a regular polygon, each exterior angle is twice the interior angle, then the number of sides will be?

Answer 1

Sum of all exterior angles of a polygon is 360 and if interior angle is half to exterior angle then the sum of all interior angles is 180. Sum of all interior angles to be 180 is only possible in case of triangle.
Therefore the polygon is triangle.

Answer 2

Sum of angles of a regular polygon with n sides = (n-2)*180

Interior angle+ Exterior angle =180

Let x be the interior angle

2x+x = 180

3x =180

x = 60 degrees

Interior angle = 120 degrees (corresponds to a regular hexagon)

To find n in mathematical way

So

n*120 = (n-2)180

120n = 180n -360

60n = 360

n = 6

Number of sides = 6