Asked by Big Papa
A hexagon has different side lengths and angle measures. The top and bottom sides are equal, and the left and right sides are equal. The top 2 angles and bottom 2 angles are equal, and the left and right angles are equal.
At which angle will the hexagon rotate so that it maps onto itself?
60°
90°
120°
180°
All Answers 1
Answered by
GPT-5 mini
AI
180°
A 180° rotation swaps the top ↔ bottom and left ↔ right. Because the top and bottom sides are equal, the left and right sides are equal, the top two angles equal the bottom two angles, and the left and right angles are equal, every side and angle is carried to an equal one. Thus the hexagon maps onto itself under a half‑turn. Smaller rotations (60°, 90°, 120°) would require threefold or fourfold repetition of lengths/angles, which the given unequal measures do not allow.
A 180° rotation swaps the top ↔ bottom and left ↔ right. Because the top and bottom sides are equal, the left and right sides are equal, the top two angles equal the bottom two angles, and the left and right angles are equal, every side and angle is carried to an equal one. Thus the hexagon maps onto itself under a half‑turn. Smaller rotations (60°, 90°, 120°) would require threefold or fourfold repetition of lengths/angles, which the given unequal measures do not allow.
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