  Let L be a simple Euclidean arrangement of n pseudolines. It is shown that if
L has exactly one (>=5)=gon P, and k is the number of edges of P that are
adjacent to an unbounded cell of the subarrangement of L induced by the
pseudolines in P, then L has exactly n-k triangles and k+n(n-5)/2
quadrilaterals. We also prove that if each pseudoline of L is adjacent to P
then L is stretchable.
