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Q: Is it possible for the exterior angles of a regular polygon to equal 30 degrees?

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7 It is not possible for a regular polygon to have exterior angles of 180 degrees or less in plane geometry

No.

A regular polygon with exterior angles of 30 degrees has: 360/30 = 12 sides

That's true if the interior angles are 108 degrees, but a regular polygon cannot have exterior angles of 108 degrees.

A regular polygon will have 360 sides with exterior angles of 181 degrees.

If its a regular 9 sided polygon then the exterior angles are 40 degrees.

The sum of all exterior angles of a polygon is 360 degrees. In a regular polygon, all of the exterior angle are equal, so there must be 360/72=5 sides of the polygon, which makes it a pentagon.

There can be no such polygon. The sum of the exterior angles of ANY polygon is 360 degrees. If it is a regular polygon, then the number of angles MUST divide 360 degrees. Since 18.95 does not divide 360, there cannot be such a polygon. If the exterior angle was 18.94737... degrees, it would be a 19-sided polygon.

Pentagon A+

8

square

The interior angles of a regular polygon cannot be less than 60 degrees so 24 degrees is not possible. ------------------------------- However a regular polygon with EXTERIOR angles of 24° has 360° ÷ 24° = 15 sides.

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