Question 767368
Let the polygon be of n sides.

Total sum of angles of a polygon of n sides = (n - 2)*180 degrees.

In a regular polygon, all internal angles are equal. 
In this case, each internal angle = 140. 
Number of internal angles = number of sides of the polygon = n.

So, 140*n = (n-2)*180 = 180*n - 360
40*n = 360
n = 9

The polygon has 9 sides.

:)