I have searched for many solutions. Finally, no one is satisfactory.
Solution 1:
as shown in here, use
\tkzMarkAngle and \tkzLabelAngle
Problem: can't draw an arrow on the arc.
Solution 2:
as show in the same place, use
\begin{scope}
\path[clip] (A) -- (E) -- (F) -- cycle;
\draw [red, fill=red!20] (A) circle (10pt);
\end{scope}
Problem: can't draw an arrow on the arc.
Solution 3:
the solution in the accepted answer might be complicated for a beginner. And I tried the code, it seems the direction of the arc is not what I expected.
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My solution:
Of course there are many other good solutions. Regarding the problem I am interested in, I came up with a simple solution. I believe many people already know about this. Just post it here for a memo.
%Requires \usetikzlibrary{calc} in the preamble
\begin{tikzpicture}
\coordinate (B) at (2.345,-1.234);
\coordinate (A) at (0,0);
\coordinate (C) at (-2.1,3.2);
\draw [densely dotted, thick] (B)--(A)--(C);
\draw (A) node[below] {$A$};
\draw (B) node[below] {$B$};
\draw (C) node[below left] {$C$};
% label the angle subtended at p1 by p2 and p3
\def\angleRadius{30pt}
% draw the arc
\draw[red,->,thick] let \p1=(A), \p2=(B), \p3=(C),
\n1={atan2(\x2-\x1,\y2-\y1)}, \n2={atan2(\x3-\x1,\y3-\y1)} in
($(\p1)!\angleRadius!(\p2)$) arc (\n1:\n2:\angleRadius);
% draw the label
\draw[red] let \p1=(A), \p2=(B), \p3=(C),
\n1={atan2(\x2-\x1,\y2-\y1)}, \n2={atan2(\x3-\x1,\y3-\y1)} in
(\p1)+(\n1/2+\n2/2:\angleRadius) node[above] {$\alpha$};
\end{tikzpicture}
Result:

We can use the following code to label the angle which is larger than 180.
\def\angleRadius{30pt}
\draw[red,->,thick] let \p1=(A), \p2=(B), \p3=(C), \n1={atan2(\x2-\x1,\y2-\y1)}, \n2={atan2(\x3-\x1,\y3-\y1)} in
($(\p1)!\angleRadius!(\p2)$) arc (\n1:\n2-360:\angleRadius);
\draw[red] let \p1=(A), \p2=(B), \p3=(C), \n1={atan2(\x2-\x1,\y2-\y1)}, \n2={atan2(\x3-\x1,\y3-\y1)} in
(\p1)+(\n1/2+\n2/2+180:\angleRadius) node[below] {$\alpha$};
The result is:

Features of the solution:
- Simple. Simply input the three points that determine the angle.
- the arc is generated by arc command. Can set the arrow of the arc and of course other properties.
- Require \usetikzlibrary{calc}, but no \usepackage{tkz-euclide}.