It is given that angle Q is 75 degrees and arc QS is 133 degrees.
Use inscribed angle theorem on angle RQS to get:
[tex]\begin{gathered} \angle RQS=\frac{1}{2}mRS \\ m(RS)=2\angle RQS \\ m(RS)=2\times75=150^{\circ} \end{gathered}[/tex]It is known that the sum of all arcs of circle is 360 degrees so it follows:
[tex]\begin{gathered} m(QS)+m(RS)+m(RQ)=360 \\ 133+150+m(RQ)=360 \\ m(RQ)=360-150-133=77^{\circ} \end{gathered}[/tex]Hence the measure of arc QR is 77 degrees.
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