Finding a Rotation

Given some shape (the green kitten) and its image under a certain rotation (the pink kitten), you have to specify this rotation. A rotation is defined by two elements: its center and angle. In each task either center or angle is fixed and the other element is to be found. As a hint, the DRAG TO FIT button shows a variable image that can be fit onto the target by adjusting the rotation manually, but the ultimate solution must be found by construction.