daedae4038 daedae4038
  • 01-03-2017
  • Mathematics
contestada

What is the smallest angle of rotational symmetry that maps a regular pentagon onto itself?

Respuesta :

wolf1728
wolf1728 wolf1728
  • 06-03-2017
72 degrees
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Answer Link
getalifecom
getalifecom getalifecom
  • 16-09-2020

Consider the regular pentagon ABCDE, with center (of mass)  O.

The central angle O is a complete angle, so its measure is 360°.

It is divided into 5 equal parts, so each of them has a measure of 360°/5=72°.

If we rotate the pentagon, with point O as the center of the rotation, we can map A to any of the other points.

The smallest angle of rotation is the angle which mas A to E, 72°.

Answer: 72°

Answer Link

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