Marking Angles

\setlength{\unitlength}{1cm}
\begin{picture}(6, 4)
  \linethickness{0.075mm}
  \multiput(0, 0)(1, 0){7}{\line(0, 1){4}}
  \multiput(0, 0)(0, 1){5}{\line(1, 0){6}}
  \thicklines
  \put(0, 0){\line(6, 1){6}}
  \put(6, 1){\line(-4, 3){4}}
  \put(2, 4){\line(-1, -2){2}}
  % arc
  % P1=(2.0/4.0) P2=(0.0/0.0) P3=(6.0/1.0) 
  % r=1.2
  \qbezier(0.5367, 1.0733)(1.0832, 0.8)
          (1.1837, 0.1973)
  % arc
  % P1=(0.0/0.0) P2=(6.0/1.0) P3=(2.0/4.0) 
  % r=1.2
  \qbezier(4.8163, 0.8027)(4.7319, 1.3092)
          (5.04, 1.72)
  % arc
  % P1=(6.0/1.0) P2=(2.0/4.0) P3=(0.0/0.0) 
  % r=1.2
  \qbezier(2.96, 3.28)(2.3591, 2.4788)
          (1.4633, 2.9267) 
  \put(0, 0){\line(3, 2){3}} 
  \put(3, 2){\line(3, -1){3}}
  % arc
  % P1=(0.0/0.0) P2=(3.0/2.0) P3=(3.0/0.0) 
  % r=0.8
  \qbezier(2.3344, 1.5562)(2.5719, 1.2)
          (3.0, 1.2) 
  % arc
  % P1=(3.0/0.0) P2=(3.0/2.0) P3=(6.0/1.0) 
  % r=0.8
  \qbezier(3.0, 1.2)(3.5766, 1.2)
          (3.7589, 1.747) 
\end{picture}