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Answer :
Final answer:
The regular pentagon can map onto itself when rotated by multiples of 72 degrees, which include only 72°, 144°, 216°, and 288° from the options presented.
Explanation:
The regular pentagon can be rotated by certain angle measures to map onto itself. These angles are multiples of the angle measure corresponding to one full rotation (360°) divided by the number of sides of the pentagon. Since a pentagon has five sides, this angle is 360° / 5 = 72°. Therefore, the pentagon can map onto itself when rotated by multiples of 72°.
Looking at the options given in the question, the correct angle measures that will allow a regular pentagon to map onto itself are:
- 72°
- 144° (2 × 72°)
- 216° (3 × 72°)
- 288° (4 × 72°)
- 360° (5 × 72°)
The options 90°, 135°, and 300° are incorrect because they are not multiples of 72°.
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