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With exterior angles measured as in the related link (extending an imaginary line out from the vertex, so that the interior and exterior at the vertex add to 180°), the sum of exterior angles of any polygon is 360°:

Interior / Exterior

______/.............

Now if you are saying the exterior angle is all the way around the vertex, then you need to add 180° for each vertex. So 360° + 57*(180°) = 10620°.

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Q: What is the sum of the exterior angles of a polygon with 57 sides?
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