Q:

How to rotate the label such that its base line is parallel to the bisector?

How to rotate the label counter clockwise such that its base line is parallel to the bisector?

\documentclass[border=0pt,pstricks]{standalone}
\usepackage{pst-eucl}
\psset{PointName=none,PointSymbol=none}
\begin{document}

\begin{pspicture}[showgrid=false](6,6)
    \pstGeonode[CurveType=polyline](1,1){A}(5,5){B}(4,1){C}
    \pstBissectBAC[linestyle=dotted,linecolor=red]{A}{B}{C}{C'}
    \pstMarkAngle[MarkAngleRadius=1.5,LabelSep=0.75]{A}{B}{C}{\tiny$180^\circ-\theta$}
\end{pspicture}

\end{document}

A:

\documentclass[border=0pt,pstricks]{standalone}
\usepackage{pst-eucl}
\psset{PointName=none,PointSymbol=none}
\begin{document}

\begin{pspicture}[showgrid=false](6,6)
    \pstGeonode[CurveType=polyline](1,1){A}(5,5){B}(4,1){C}
    \pstBissectBAC[linestyle=dotted,linecolor=red]{A}{B}{C}{B'}
    \pstMarkAngle[MarkAngleRadius=1.6,LabelSep=1]{A}{B}{C}{}
    \pcline[linestyle=none](B')(B)\ncput[nrot=:U,npos=0.84]{\tiny$180^\circ-\theta$}
\end{pspicture}

\end{document}

a solution without knowing B'
\documentclass{article}
\usepackage{pst-eucl}
\begin{document}    
\begin{pspicture}[showgrid=false](6,6)
    \pstGeonode[CurveType=polyline](1,1){A}(5,5){B}(4,1){C}
    \pstMarkAngle[MarkAngleRadius=1.6,LabelSep=1]{A}{B}{C}{}
  \pcline[linestyle=none](!
    \psGetNodeCenter{A} \psGetNodeCenter{B} \psGetNodeCenter{C}      
    /LengthBA B.x A.x sub dup mul B.y A.y sub dup mul add sqrt def     
    /LengthBC C.x A.x sub dup mul C.y A.y sub dup mul add sqrt def     
    /Factor LengthBC LengthBA div def     
    A.x B.x sub Factor mul B.x add /A.x ED     
    A.y B.y sub Factor mul B.y add /A.y ED     
    A.x C.x add 2 div A.y C.y add 2 div )(B)\ncput[nrot=:U,npos=0.84]{\tiny$180^\circ-\theta$} 
\end{pspicture}

\end{document}

A:

I got the solution even though it is not elegant enough.

\documentclass[border=0pt,pstricks]{standalone}
\usepackage{pst-eucl}
\psset{PointName=none,PointSymbol=none}
\begin{document}

\begin{pspicture}[showgrid=false](6,6)
    \pstGeonode[CurveType=polyline](1,1){A}(5,5){B}(4,1){C}
    \pstMarkAngle[MarkAngleRadius=1.6,LabelSep=1]{A}{B}{C}{\rput{(B)}(0,0){\tiny$180^\circ-\theta$}}
\end{pspicture}

\end{document}

Clockwise rotation:

\documentclass[border=0pt,pstricks]{standalone}
\usepackage{pst-eucl}
\psset{PointName=none,PointSymbol=none}
\begin{document}

\begin{pspicture}[showgrid=false](6,6)
    \pstGeonode[CurveType=polyline](1,1){A}(5,5){B}(4,1){C}
    \pstMarkAngle[MarkAngleRadius=1.6,LabelSep=1]{A}{B}{C}{\rput{!\psGetNodeCenter{B} B.y B.x atan 180 sub}(0,0){\tiny$180^\circ-\theta$}}
\end{pspicture}

\end{document}

