Plane graphs with straight edges whose bounded faces are acute triangles

Let $T_n$ denote a graph obtained as a triangulation of an $n$-gon in the plane. A cycle of $T_n$ is called an enclosing cycle if at least one vertex lies inside the cycle. In this paper it is proved that a triangulation $T_n$ admits a straight-line embedding in the plane whose bounded faces are all acute triangles if and only if $T_n$ has no enclosing cycle of length $\le 4$. Those $T_n$ that admit straight-line embeddings in the plane without obtuse triangles are also characterized