The diagonals of a rhombus intersect each other at the midpoints and they are also perpendicular . So at the smallest angle we have a right angled triangle with legs 6 and 3.5. Also this smallest angle (x) is bisected by the diagonal. so we have:-
Central angle of a regular polygon: Ф = 360° : n. If n=12: Ф = 360° : 12 = 30° At the angle of rotation Ф = 30° the image of the polygon will coincide with the preimage.