Abstract. Consider a pencil of rays in the Euclidean or Hyperbolic plane. The question may arise whether a polygon with equal angles can be constructed in such a way that the vertices are located on the given set of rays. We will discuss the solutions for triangles and quadrilaterals where the conditions are exactly given.

AMS Subject Classification (1991): 51M20

Received May 16, 2006, and in revised form January 16, 2007. (Registered under 8/2006.)