  Let $S_g$ be a closed orientable surface of genus $g \geq 2$, and let
$\mathcal{T}_g$ be the Teichm\"uller space of $S_g$. Let $\mathcal{H}_g$
denotes the space of all hyperelliptic surfaces of genus $g$. For $g\geq 3$, we
have proved that $\mathcal{T}_g$ can be parametrized by $6g-5$ angle
parameters. We also prove that for $g\geq 2$, $\mathcal{H}_g$ can be
parametrized by $4g-2$ angle parameters.
