绘制带箭头的圆弧

Question

下面的代码（使用pict2e包）似乎实现了我的预期，但我想做一些进一步的编辑，添加一些其他行并以不同的方式标记角度。

当角彼此相邻（共享一个公共顶点）时，可以通过两条射线之间以顶点为中心的圆弧明确地表示出从顶点发出的哪对射线对应于哪些给出角名称的标签，圆弧与顶点之间标有角标签，圆弧两端的箭头清楚地表明哪两条射线限制了带有该标签的圆弧。

是否有简单的方法可以绘制这种带箭头的弧线？

\documentclass{article}

\usepackage{pict2e}

\begin{document}

\begin{figure}[h]
\setlength{\unitlength}{0.5mm}
\begin{picture}(200,180)(-35,0)
\label{hexagon}
\put(90,100){\circle{180}}      % left big circle
\put(90,190){\circle*{4}}       % dot at top of circle 
\put(144,172){\circle*{4}}      % dot at
\put(162,46){\circle*{4}}       % dot at
\put(90,10){\circle*{4}}        % dot at bottom of circle
\put(0,100){\circle*{4}}
\put(36,172){\circle*{4}}

\put(90,10){\line(-1,1){90}}    % line
\put(0,100){\line(1,2){36}}
\put(36,172){\line(3,1){54}}
\put(90,190){\line(3,-1){54}}
\put(144,172){\line(1,-7){18}}

\put(90,10){\line(2,1){72}}

\put(0,100){\line(1,1){90}}
\put(0,100){\line(2,1){144}}
\put(0,100){\line(3,-1){162}}

\put(90,10){\line(-1,3){54}}
\put(90,10){\line(0,1){180}}
\put(90,10){\line(1,3){54}}


\put(15,121){$\delta$}
\put(20,115){$\gamma$}
\put(22,100){$\beta$}
\put(18,85){$\alpha$}

\put(103,26){$\beta$}
\put(92,34){$\gamma$}
\put(85,34){$\delta$}
\put(75,30){$\varepsilon$}

\put(36,172){\line(1,0){108}}
\put(36,172){\line(1,-1){126}}
\put(90,190){\line(1,-2){72}}

\put(149,76){$\gamma$}
\put(140,71){$\delta$}
\put(135,59){$\varepsilon$}
\put(137,42){$\zeta$}

\put(113,173){$\delta$}
\put(116,164){$\varepsilon$}
\put(127,152){$\zeta$}
\put(139,146){$\alpha$}


\end{picture}
\caption{}
\label{diagonals}
\end{figure}

\end{document}