[tex]\begin{gathered} \angle PRQ=90^0(\text{ angle in a semi-circle)} \\ \angle QOR=50^0(angle\text{ subtended by the arc QR at the centre of the circle)} \\ \angle\text{QOR}=2\angle RPQ(\text{ angle at centre is twice angle at circumference)} \\ 50=2\angle RPQ \\ \angle RPQ=\frac{50}{2} \\ \angle RPQ=25^0 \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} \angle RPQ+\angle PRQ+\angle PQR=180^0(sum\text{ of interior angles in triangle PQR)} \\ 25+90+\angle PQR=180^0 \\ 115+\angle PQR=180 \\ \angle PQR=180-115 \\ \angle PQR=65^0 \end{gathered}[/tex]
Hence, the measure of angle PQR is 65 degrees.
