Join JH and KH.
You did that so you could measure or calculate the size of <JHK. There are 5 such central angles in a pentagon. If you drew a little circle with H as the center and you went around the circle once, you would have traveled 360 degrees. So <JHK = 360/5 = 72. Make sure you understand that before you read on.
Ok here's the trick. 144 = 2*72. That means that when you rotate the pentagon, you rotate it through Two central angles.
What will happen is that Point J will wind up at Point L and Point K will sit where N is right now. All the points not mentioned will do the same thing. They will move two points clockwise.