A polygon is called good if it satisfies the following conditions: (i) All its angles are in $(0,\pi)$ or in $(\pi ,2\pi)$, (ii) It is not self-intersecing, (iii) For any three sides, two are parallel and equal. Find all $n$ for which there exists a good $n$-gon.
Problem
Source: North Macedonian Mathematical Olympiad 1996 p4
Tags: geometry, combinatorial geometry, polygon, parallel