Excellent. There's already a script out there that does this, but it does not work very well for me. Specifically, it often selects a vertex behind the one I want, and then gives an incorrect angle. It would be much better if you could restrict it to act only in a given plane, like the native protractor tool.
The existing script by Didier Bur is called dim_angle.rb, and can be found here: http://www.crai.archi.fr/RubyLibraryDepot/Ruby/em_arc_page.htm