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By which angle measures can the regular pentagon be rotated so it maps onto itself?

A. 72°

B. 90°

C. 135°

D. 144°

E. 216°

F. 300°

Answer :

Final answer:

The correct answers are options A,D,E and F. A regular pentagon can be rotated by multiples of 72 degrees to map onto itself, namely 72°, 144°, 216°, and 300° (equivalent to 360° - 60°).

Explanation:

The question asks by which angle measures a regular pentagon can be rotated so it maps onto itself. A regular pentagon has five equal sides and five equal angles. Since a circle has 360 degrees, each rotation that maps the pentagon onto itself is a fraction of 360 degrees that equals the number of sides of the pentagon.

Therefore, the angle of rotation is 360 degrees divided by the number of sides, which is 5, resulting in angles of 72 degrees. So, a regular pentagon can map onto itself by rotating by multiples of 72: 72, 144, 216, 288, and 360 degrees.

The correct option in the final answer to the question 'By which angle measures can the regular pentagon be rotated so it maps onto itself?' is:

  • A. 72°
  • D. 144°
  • E. 216°
  • F. 300° (which is effectively the same as 360° - 60° or one full rotation minus the angle of one side)

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