∠P + ∠Q = 180° (Angles on the same side of transversal)

∠P + 130° = 180°

∠P = 50°

∠R + ∠S = 180° (Angles on the same side of transversal)

90° + ∠R = 180°

∠S = 90°

Yes. There is one more method to find the measure of m∠P.

m∠R and m∠Q are given. After finding m∠S, the angle sum property of a quadrilateral can be applied to find m∠P.