Is there a directed angle symbol?

Question

Is there a symbol for an angle measured in counter clockwise direction? That would be a directed round arrow for ccw (or cw) direction added to $\angle$.

Something like this:

Answer 1

With tikz

\documentclass{standalone}
\usepackage{tikz}
\def\angle{\tikz[baseline=0mm]{\draw(30:1)--(0,0)--(1,0);\draw->arc(-10:45:.75);}}
\begin{document}
This \angle\ is an angle.
\end{document}

Answer 2

From an idea of @egreg's answer, How to write a character overlapping another character, with some little adjustments.

\documentclass[12pt]{article}
\usepackage{amssymb,mathabx}
\usepackage{scalerel}
\makeatletter
\DeclareRobustCommand{\roundarrowangle}[1]{% arrow strike
  {\vphantom{#1}\mathpalette\erel@as{#1}}%
}
\newcommand{\erel@as}[2]{%
  \ooalign{\hfil$\m@th#1\angle$\hfil\cr\hfil$\m@th#1#2$\hfil\cr}%
}
\makeatother
\usepackage{graphicx}
\newcommand{\rcarrow}{\rotatebox[origin=c]{-45}{$\mkern-4mu\scaleobj{.8}{\curvearrowleft}$}}
\begin{document}
$\roundarrowangle{\rcarrow}$
\end{document}