Question 53

$$\triangle PQR$$ is inscribed in a circle with center O. PO is produced to meet QR at U and the circle at S, and $$PT \perp QR$$, where T lies between Q and U. If $$\angle Q = 70^\circ$$ and $$\angle R = 55^\circ$$, then what is the measure (in degrees) of $$\angle TPS$$?

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