To determine the measure of angle PSR in cyclic quadrilateral PQRS, we can use the Law of Cosines. First, we find angle QPR using the Law of Cosines: cos(QPR) = (QR^2 + PR^2 - PQ^2) / (2 * QR * PR). Next, we find angle PSR by subtracting angle QPR from 180 degrees since the sum of opposite angles in a cyclic quadrilateral is 180 degrees. Finally, we can find angle SPR by subtracting angle PSR from 180 degrees. Calculating these angles will give us the required measurements.
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