1.15 Rotational Symmetry

triangle' is triangle rotated around point O. Use the slider and change the angle of rotation until triangle' and triangle are in the same position.
What angles of rotation result in triangle' being in the exact same location as triangle?
square' is square rotated around point O. Use the slider and change the angle of rotation until square' and square are in the same position.
What angles of rotation result in square' being in the exact same location as square?
hexagon' is hexagon rotated around the point O. Use the slider and change the angle of rotation until hexagon' and hexagon are in the same position.
What angles of rotation result in hexagon' being in the exact same location as hexagon?
triangle' is triangle rotated around point O. You can move point O if needed.
Can you find a position of O and an angle of rotation where triangle' is in exactly the same position as triangle?
CHALLENGE
What are the angles of rotation of an 8 sided regular polygon (octagon)?
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Information: 1.15 Rotational Symmetry