Question

describe the rotational symmetry or symmetries of the figure. choose the correct answer below. \
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a. 180° \
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b. 90°, 180°, 270° \
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c. 120°, 240° \
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d. the figure does not have rotational symmetry. \
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help me solve this \
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Explanation:

Step1: Analyze Rotational Symmetry

Rotational symmetry means a figure maps onto itself after a rotation. For the given figure (a four - petal - like shape with squares), we check rotation angles. A full rotation is \(360^{\circ}\). If we rotate the figure by \(90^{\circ}\), \(180^{\circ}\), \(270^{\circ}\), it should map onto itself. Let's verify:

• Rotate by \(90^{\circ}\): The square and the surrounding shapes will align with the next petal.
• Rotate by \(180^{\circ}\): The figure will be upside - down but still match the original.
• Rotate by \(270^{\circ}\): Similar to \(90^{\circ}\) rotation in the other direction, it will align.

Step2: Evaluate Options

• Option A: Only \(180^{\circ}\) is given, but we know \(90^{\circ}\) and \(270^{\circ}\) also work, so A is wrong.
• Option B: \(90^{\circ}\), \(180^{\circ}\), \(270^{\circ}\) are all angles by which the figure maps onto itself.
• Option C: \(120^{\circ}\) and \(240^{\circ}\) rotations will not map the figure onto itself (since \(360\div4 = 90\), the rotational symmetry angles should be multiples of \(90^{\circ}\)), so C is wrong.
• Option D: The figure does have rotational symmetry, so D is wrong.

Answer:

B. \(90^{\circ}, 180^{\circ}, 270^{\circ}\)