Gfyuki

I'm new to TikZ and I'm trying to label the angle between two intersecting circles, as seen in red in the following picture,

Below is my code so far which makes the following diagram,

documentclass[border=5pt]{standalone}

usepackage{tikz,tikz-3dplot}

begin{document}

tdplotsetmaincoords{70}{110}

begin{tikzpicture}[tdplot_main_coords,scale=5]

  pgfmathsetmacro{r}{1}

  pgfmathsetmacro{O}{60} 

  pgfmathsetmacro{i}{45} 



  coordinate (O) at (0,0,0);

  tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE



  tdplotsetrotatedcoords{-O}{i}{0}

  tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO

end{tikzpicture}

end{document}

I appreciate the help!

Welcome to TeX.SE! Here is a proposal. I do not know what the absolutely correct way is. I do, of course, know how to indicate an angle between two lines on a plane. But here we deal with an angle line between two curves. Is it supposed to run on the sphere? If so, on a great circle? In the limit of an infinitely large sphere this prescription will not reproduce our standard conventions in the plane, rather it will yield a straight line. Since this seems not to be well-defined, I just computed the intersection, I, of the two circles and points on the two circles that are away from the intersection by the same amount, I1 and I2. And then I connected those with an arc that "looks right".

documentclass[border=5pt]{standalone}

usepackage{tikz,tikz-3dplot}

begin{document}

tdplotsetmaincoords{70}{110}

begin{tikzpicture}[tdplot_main_coords,scale=5]

  pgfmathsetmacro{r}{1}

  pgfmathsetmacro{O}{60} 

  pgfmathsetmacro{i}{45} 

  pgfmathsetmacro{dang}{-30} 



  coordinate (O) at (0,0,0);

  tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE



  tdplotsetrotatedcoords{-O}{i}{0}

  tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO



  path  ({sin(O)},{cos(O)},{0}) coordinate (I);

  path  ({sin(O+dang)},{cos(O+dang)},{0}) coordinate (I1);

  path[tdplot_rotated_coords]  ({sin(dang)},{cos(dang)},{0})

  coordinate (I2);

  draw (I1) to[out=95,in=-50] node[pos=0.5,right] {$i^circ$} (I2);

end{tikzpicture}

end{document}