If integer n is the number of sides of the polygon, the angle at the centre would be 360/n, the apex of n isosceles triangles. 180-360/n is divided between 2 remaining angles, so the equal angles are each 90-180/n. The interior angle of the polygon is 2(90-180/n)=180-360/n=180(1-2/n). We can find n if 180(1-2/n)=130, 1-2/n=13/18, 2/n=5/18, n=36/5=7.2, not an integer. Therefore no regular polygon can have interior angles of 130º.