Hexagon Rotation Puzzle

hexagon' is hexagon rotated around the point O.[br][br]Use the slider and change the angle of rotation until hexagon' and hexagon are in the same position.[br]
What angles of rotation result in hexagon' being in the exact same location as hexagon?
What are the interior angles of the regular hexagon?
What are the exterior angles of the regular hexagon?
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Information: Hexagon Rotation Puzzle