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\addplot [color=red, line width=2.0pt, forget plot]
  table[row sep=crcr]{%
  	\coordinate (T) at (0cm, 1cm) {};
  	\coordinate (A) at (0cm, 0cm) {}; 
  	\coordinate (D) at (3cm,-2cm) {};
  	\draw (T) -- (A) -- (D)
  	pic [draw, "$\alpha_Z$",angle radius=.8cm,angle eccentricity=.4] {angle=T--A--D}; 
};

% This file was created by matlab2tikz.
%
%The latest updates can be retrieved from
%  http://www.mathworks.com/matlabcentral/fileexchange/22022-matlab2tikz-matlab2tikz
%where you can also make suggestions and rate matlab2tikz.
%
\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
\definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
%
\begin{tikzpicture}

\begin{axis}[%
width=0.742\textwidth,
height=0.411\textwidth,
at={(0\textwidth,0\textwidth)},
scale only axis,
xmin=-20,
xmax=100,
xlabel style={font=\color{white!15!black}},
xlabel={X Position [px]},
ymin=0,
ymax=80,
ylabel style={font=\color{white!15!black}},
ylabel={Y Position [px]},
axis background/.style={fill=white},
legend style={at={(0.173,0.797)}, anchor=south west, legend cell align=left, align=left, draw=white!15!black}
]
\addplot [color=mycolor1, line width=2.0pt]
  table[row sep=crcr]{%
0	0\\
100	0\\
100	50\\
0	50\\
0	0\\
};
\addlegendentry{Reales Bild}

\addplot [color=mycolor2, line width=2.0pt]
  table[row sep=crcr]{%
0	0\\
96.5925826289068	25.8819045102521\\
83.6516303737808	74.1781958247055\\
-12.940952255126	48.2962913144534\\
0	0\\
};
\addlegendentry{Verdrehtes Bild}
\end{axis}
\end{tikzpicture}%

\usepackage{graphicx, epsfig, subfigure, pstricks, tikz, calc, pgfplots}
\usetikzlibrary{angles,quotes}

\documentclass{article}
\usepackage{amssymb}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}% <- wichtig: direkt nach dem Laden von pgfplots setzen
\usetikzlibrary{angles}

\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}
\definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}

\begin{document}

\begin{tikzpicture} 
\begin{axis}[% 
width=0.742\textwidth, 
height=0.495\textwidth,% geändert, damit x- und y-Achse gleiche Einheit verwenden
%at={(0\textwidth,0\textwidth)},% überflüssig
scale only axis, 
xmin=-20, 
xmax=100, 
%xlabel style={font=\color{white!15!black}}, 
xlabel={X Position [px]}, 
ymin=0, 
ymax=80, 
%ylabel style={font=\color{white!15!black}}, 
ylabel={Y Position [px]}, 
%axis background/.style={fill=white}, 
legend style={at={(0.05,0.797)}, anchor=south west, legend cell align=left, align=left, draw=white!15!black} 
]
\addplot [color=mycolor1, line width=2.0pt] 
  table[row sep=crcr]{% 
0   0\\ 
100   0\\ 
100   50\\ 
0   50\\ 
0   0\\ 
}; 
\addlegendentry{Reales Bild} 

\addplot [color=mycolor2, line width=2.0pt] 
  table[row sep=crcr]{% 
0   0\\ 
96.5925826289068   25.8819045102521\\ 
83.6516303737808   74.1781958247055\\ 
-12.940952255126   48.2962913144534\\ 
0   0\\ 
}; 
\addlegendentry{Verdrehtes Bild}
% Winkel einzeichnen:
\path
  (100,0) coordinate (A)
  (0,0) coordinate (O)
  (96.5925826289068,25.8819045102521) coordinate (A')
;
\pic[draw=red,line width=2pt,angle radius=2.5cm,pic text=$\alpha$,angle eccentricity=.7]{angle=A--O--A'};

\end{axis} 
\end{tikzpicture}% 
\end{document}