Time to use pic
\documentclass{article}
%\usepackage{xcolor,pict2e}% to allow any radius
\usepackage{tikz}
\tikzset{pics/myarc/.style args={inner #1 and outer #2}{
code={
\draw[very thick,dashed, #1] (1,0) arc (0:90:1cm);
\draw[very thick] (0,1) -- (0,2);
\draw[very thick,dashed, #2] (0,2) arc (90:0:2cm);
\draw[very thick] (2,0) -- (1,0);
}
}}
\begin{document}
\begin{tikzpicture}
\draw[very thick,<->] (-6,0) -- (6,0)node[anchor=north west] {$x$};
\pic [draw,rotate=-45] {myarc={inner red and outer blue}};
\pic [draw, rotate=45] {myarc={inner olive and outer magenta}};
\pic [draw, rotate=135] {myarc={inner blue and outer teal}};
\pic [draw, rotate=225] {myarc={inner cyan and outer orange}};
\end{tikzpicture}
\end{document}

With filling:
\documentclass{article}
%\usepackage{xcolor,pict2e}% to allow any radius
\usepackage{tikz}
\tikzset{pics/myarc/.style args={inner #1 and outer #2 with fill #3}{
code={
\draw[very thick,dashed, #1] (1,0) arc (0:90:1cm);
\draw[very thick] (0,1) -- (0,2);
\draw[very thick,dashed, #2] (0,2) arc (90:0:2cm);
\draw[very thick] (2,0) -- (1,0);
\fill[#3] (1,0) arc (0:90:1cm) -- (0,2) arc (90:0:2cm) -- cycle;
}
}}
\begin{document}
\begin{tikzpicture}
\draw[very thick,<->] (-6,0) -- (6,0)node[anchor=north west] {$x$};
\pic [draw,rotate=-45] {myarc={inner red and outer blue with fill red!20}};
\pic [draw, rotate=45] {myarc={inner olive and outer magenta with fill green!20}};
\pic [draw, rotate=135] {myarc={inner blue and outer teal with fill olive!30}};
\pic [draw, rotate=225] {myarc={inner cyan and outer orange with fill brown!20}};
\end{tikzpicture}
\end{document}

Now the confusion as the code and picture in OP are not the same. What is needed actually?
\documentclass{article}
%\usepackage{xcolor,pict2e}% to allow any radius
\usepackage{tikz}
\tikzset{pics/myarc/.style args={#1}{
code={
\draw[very thick,#1] (2,0) arc(0:90:2cm);
}
}}
\begin{document}
\begin{tikzpicture}
\draw[very thick,<->] (-6,0) -- (6,0)node[anchor=north west] {$x$};
\foreach \rot/\col in {-45/green,45/blue,135/red,225/blue}{
\pic [draw,rotate=\rot] {myarc={\col}};
}
\end{tikzpicture}
\end{document}

pict2e
supposed to do? – cfr Apr 20 '15 at 23:30