Square Rotation Puzzle

square' is square rotated around point O.[br][br]Use the slider and change the angle of rotation until square' and square are in the same position.[br]
What angles of rotation result in square' being in the exact same location as square?
What are the interior angles of a square?
What are the exterior angles of a square?
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– Aja Wright, David Wees

Information: Square Rotation Puzzle