Question 756847
{{{drawing(300,300,-1.1,1.1,-1.1,1.1,
circle(0,0,1),locate(-0.07,0.05,O),
locate(0.51,0.95,A),locate(0.5,-0.86,B),
line(0,0,0.5,0.866),line(0,0,0.5,-0.866),
line(-1,0,0.5,0.866),line(-1,0,0.5,-0.866),
line(-0.707,0.707,0.5,0.866),line(-0.707,0.707,0.5,-0.866),
locate(-1.07,0.05,P),locate(-0.78,0.76,Q),
red(line(1,0,0.5,0.866)),red(line(1,0,0.5,-0.866)),
locate(1,0.05,red(R))
)}}} Angle AOB and the arc AB it subtends measure {{{120^o}}}
Angles APB and AQB measure {{{120^o/2=highlight(60^o)}}}, half the measure of the arc they subtend.
I believe that was the expected answer.
 
Angle ARB measures {{{240^o/2=120^o}}} because it subtends and arc measuring {{{360^o-120^o=240^o}}}, but I do not think it was the kind of angle that was in the mind of the person who proposed that problem.