Known angle QSP = 90 degree. We need to find difference between angle PQR and PRS. Let PQR be x degree and PRS be y degree. We need the value of (y-x) degree.
Statement A: angle QPR is 30 degree.
Using the exterior angle concept, we know that angle QPR + angle PQR = angle PRS.
=> 30 + angle PQR = angle PRS => 30 + x = y => y-x = 30 degree. Hence we have got the required angle. Sufficient.
Statement B: angle PQR and PRQ = 150 degree.
In the triangle QPR, sum of the interior angles is 180 degree. That is angle QPR + angle PQR + angle PRQ = 180 degree.
Hence angle QPR = 180 - 150 = 30 degree. Here we have got the same angle as the one mentioned in statement A. Also we have proved that Statement A is sufficient. Hence Statement B is also sufficient.
Answer is D.
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