How to add a white background to an angle label in Tikz?
Use "$\alpha$"{fill=white}
instead of "$\alpha$"
in \pic
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,patterns,angles,quotes,arrows}
\begin{document}
\begin{figure}
\begin{center}
\begin{tikzpicture}
%Define coordinates
\coordinate (origin) at (0,0);
\coordinate (bhat) at (0,5);
\coordinate (zetahat) at (5,0);
\coordinate (vector) at (3,4);
\coordinate (normal) at (1.581,4.743);
%Draw axes
\draw[thick, <->] (bhat) node[above]{$\hat{b}$} -- (origin) -- (zetahat) node[right]{$\hat{\zeta}$};
%Draw vector
\draw[thick, ->, blue] (origin) -- (vector) node[above]{$\vec{v_r}$};
%N vector
\draw[thick, dotted, ->] (origin) -- (normal) node[above]{$\hat{n}$};
%Draw angle
\pic [draw, "$\alpha$"{fill=white}, angle eccentricity = 1.2, angle radius = 1.5cm, thick] {angle = vector--origin--bhat};
\end{tikzpicture}
\caption{Pitch angle $\alpha$ is equal to $2\theta_{bn}$, showing specular reflection}
\label{fig:Pitch Angle}
\end{center}
\end{figure}
\end{document}
A PSTricks solution only for comparison purposes. A single *
does the job (making the label background solid).
\documentclass[pstricks,12pt]{standalone}
\begin{document}
\pspicture(-1,-1)(6,6)
\psline{<->}(0,5)(0,0)(5,0)
\psline{->}(5;60)
\psline[linestyle=dotted,dotsep=1pt]{->}(5;75)
\uput[90](0,5){$\hat{b}$}
\uput[0](5,0){$\hat{\zeta}$}
\uput[60](5;60){$\vec{v}_r$}
\uput[75](5;75){$\hat{n}$}
\uput*{2.5}[75](0,0){$\alpha$}
\psarc(0,0){2}{60}{90}
\endpspicture
\end{document}