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