\documentclass[12pt]{extarticle}
\usepackage[paperwidth=8.6cm, paperheight=5.55cm, top=0cm, bottom=0cm, left=0cm, right=0cm]{geometry}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,positioning,calc}
\tikzset{circle1/.style={draw, circle, minimum size = 1.5mm}}
\tikzset{pics/perp/.style={code={\draw[-] (0,0) -- (1,0) (0,-0.5) -- (0,0.5);}},
pics/line/.style={code={\draw[-] (0,0) -- (1,0);}}}
\begin{document}
\begin{tikzpicture}[auto]
\node (first) [circle1] {first};
\node (second) [circle1, below right=1.5cm and 5.5cm of first] {second};
\draw[->, thick] (first.0) -- pic[yshift=3mm,scale=0.3]{line} (second.135);
\draw[->, thick] (first.0) |- pic[yshift=-3mm,scale=0.3]{perp} (second.160);
\draw[->, thick,red] let \p1=(first.east), \p2=(second.120) in
(first.east) -- ++({\x2-\x1-\y1+\y2},0) -- (second.120);
\end{tikzpicture}
\end{document}

After the suggestion by EL_DON to generalize: here is a version with an edge style.
\documentclass[12pt]{extarticle}
\usepackage[paperwidth=8.6cm, paperheight=5.55cm, top=0cm, bottom=0cm, left=0cm, right=0cm]{geometry}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,positioning,calc}
\tikzset{circle1/.style={draw, circle, minimum size = 1.5mm}}
\tikzset{pics/perp/.style={code={\draw[-] (0,0) -- (1,0) (0,-0.5) -- (0,0.5);}},
pics/line/.style={code={\draw[-] (0,0) -- (1,0);}}}
\begin{document}
\begin{tikzpicture}[auto,connect with angle/.style=
{to path={let \p1=(\tikztostart),
\p2=(\tikztotarget) in -- ++({\x2-\x1-(\y1-\y2)*tan(#1-90)},0) -- (\tikztotarget)}}]
\node (first) [circle1] {first};
\node (second) [circle1, below right=1.5cm and 5.5cm of first] {second};
\draw[->, thick] (first.0) -- pic[yshift=3mm,scale=0.3]{line} (second.135);
\draw[->, thick] (first.0) |- pic[yshift=-3mm,scale=0.3]{perp} (second.160);
\draw[red,-latex] (first.east) edge[connect with angle=135] (second.120);
\draw[blue,-latex] (first.east) edge[connect with angle=105] (second.120);
\end{tikzpicture}
\end{document}

Here, by EL_DON's convention, the angle is the angle between the two stretches. Other conventions may be accounted for by adjusting tan(#1-90) appropriately.
\newcommand\exitangle{135}and then changing({\x2-\x1-\y1+\y2},0)to({\x2-\x1-(\y1-\y2)*tan(\exitangle-90)},0)and also using\exitanglein contexts like\p2=(second.\exitangle). – EL_DON Jun 28 '18 at 20:37connect with anglelike this would be a lot cleaner in a picture that needed several of these angled arrows. – EL_DON Jun 28 '18 at 21:16