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a n-gon by choosing points on sides of regular n-gon, equal angles, not regular

Source: 2013 Portugal MO p6

October 9, 2020
combinatoricsRegularequal anglescombinatorial geometrygeometry

Problem Statement

In each side of a regular polygon with nn sides, we choose a point different from the vertices and we obtain a new polygon of nn sides. For which values of nn can we obtain a polygon such that the internal angles are all equal but the polygon isn't regular?
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