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

The smallest angle of rotational symmetry for a regular pentagon is 72°.

Why it’s 72°

A regular pentagon has 5 equal sides and 5 equal angles, so a full turn of 360° is split evenly into 5 matching positions.

So the smallest angle that maps it onto itself is:

360∘5=72∘\frac{360^\circ}{5}=72^\circ 5360∘​=72∘

Each further rotational symmetry is then 72°, 144°, 216°, 288°, and finally 360° bringing it back to the start.

TL;DR: The answer to “what is the smallest angle of rotational symmetry that maps a regular pentagon onto itself?” is 72°.

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