if the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?10122024

The polygon has 20 sides.

Skills needed: Polygon Geometry

Step-by-step explanation:

1) We need to first understand what "angle of rotation" is. Angle of rotation essentially is any angle measure that one can rotate a polygon by, but still have the same polygon.

2) Noticing the pattern: The calculation for the smallest angle of rotation in a regular polygon is , with being the # of sides.

Formula: (, )

3) For this problem, we are given the angle of rotation. We need to find .

Multiply by n on both sides:

Divide by 18 on both sides:

Therefore, the polygon, which is regular, has 20 sides.

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