$\begin{align}  & \text{consider }\Delta PSQ \\ & \angle PSQ={{90}^{o}}\text{    }\!\!\{\!\!\text{ angle in semicircle }\!\!\}\!\!\text{ } \\ & \angle QSR={{145}^{o}}-{{90}^{o}}={{55}^{o}} \\ & \text{Join point }P\text{ and }Q\text{ together} \\ & \text{Consider }\Delta QRS\text{ and }\Delta RQP\ \text{which has }QR\text{ has its base} \\ & \angle RPQ=\angle QSR={{55}^{o}}\text{    }\!\!\{\!\!\text{ Angle on the same segment and base }\!\!\}\!\!\text{ } \\ & \angle RPO=x={{55}^{o}} \\\end{align}$