See accompanying image for the three required items indicated in blue.
First,
angle RTS
=angle subtended by chord RS on the circumference
=half the arc RS = 46/2=23 °
Next, Arc ST is the supplement of arc RS, since RXT is a diameter.
so
arc ST = 180-46=134 °
Finally, angle RST sits on a diameter, hence it equals 90 °.
So angle RSQ=90-71=19 °.
Since angle subtended by chord RQ on the circumference is half that of arc RQ, we have arc RQ=2*angle RSQ=2*19=38 °
