If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have? 10 12 20 24

The polygon has 20 sides (Icosagon)

Step-by-step explanation:

As the smallest angle of rotation for a regular polygon is 18°, so a 18° rotation yields the same figure.

According to the attachment, the side AB subtends an angle of 18° at the centre. That is why a 18° rotation generates the same figure.

According to the properties of regular polygon,

And

(as the radius of a regular polygon bisects the interior angle)

As in the triangle OAB,

So,

So, interior angle of polygon is 162°

We know that, the interior angle of regular polygon with n side is,

Hence,

Therefore, the polygon has 20 sides (Icosagon)