What is the order of rotational symmetry and angle of rotation symmetry for this design?

Question

9. What is the order of rotational symmetry and angle of rotation symmetry for this design?
a. 4, 90° b. 6, 120° c. 8, 60° d. 8, 45°
10. Which figure shows the rotation image of pentagon A after a 216° clockwise rotation about its centre?
a. Figure iii b. Figure i c. Figure iv d. Figure ii

SnapAndSolve AI · Accepted Answer

The design has 8 identical sections, so the order of rotational symmetry is 8. The angle of rotation symmetry is 360° divided by the order, which is 45°. Therefore, the answer is d. 8, 45°.
A 216° clockwise rotation is equivalent to a 360° - 216° = 144° counterclockwise rotation. Since the pentagon has 5 sides, each rotation of 72° (360°/5) will bring it to a new position. A 144° counterclockwise rotation is equivalent to two 72° rotations. The correct figure is c. Figure iv.

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What is the order of rotational symmetry and angle of rotation symmetry for this design?

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