A regular polygon has possible angles of rotational symmetry of 20 degrees , 40 degrees , and 80 degrees How many sides does the polygon have?

For a regular polygon with 18 sides, the smallest rotational symmetry angle is 360° ÷ 18 = 20°. Rotating by 20°, 40° (twice that), or 80° (four times that) maps the polygon onto itself. So the polygon has 18 sides.

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