tikz library angle - Winkel schließt nicht

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{angles,quotes,intersections}
\tikzset{
  angle radius=0.75cm
}
\begin{document}

\section*{Scheitelwinkel}
\begin{tikzpicture}
  \draw[name path=A] (0,0) coordinate (A) -- (5,0) coordinate (B);
  \draw[name path=B] (1,2) coordinate (C) -- (3,-1) coordinate (D);
  \path[name intersections={of=A and B,name=i}];
  \draw pic["$\alpha$", draw=red, ->] {angle=D--i-1--B};
  \draw pic["$\alpha'$", draw=blue, ->] {angle=C--i-1--A};
\end{tikzpicture}

\section*{Stufenwinkel}
\begin{tikzpicture}
  \draw[name path=A] (0,0) coordinate (A) -- (5,0) coordinate (B);
  \draw[name path=B] (3,2) coordinate (C) -- (1,-1) coordinate (D);
  \draw[name path=C] (0,1) coordinate (E) -- (5,1) coordinate (F);
  \path[name intersections={of=A and B,name=i}]; % <--
  \path[name intersections={of=B and C,name=j}];
  \draw pic["$\alpha$", draw=red, ->] {angle=B--i-1--C};
  \draw pic["$\alpha'$", draw=blue, ->] {angle=C--j-1--E};
\end{tikzpicture}
\end{document}