  We prove that every planar straight line graph with $n$ vertices has a
conforming quadrilateral mesh with $O(n^2)$ elements, all angles $\leq
120^\circ$ and all new angles $\geq 60^\circ$. Both the complexity and the
angle bounds are sharp. Moreover, all but $O(n)$ of the angles may be taken in
a smaller interval, say $[89^\circ, 91^\circ]$.
