UPSC CDS Math Lines and Angles Questions

PQ || RS and PR || QS,
Therefore, PQRS is a parallelogram.
∠QSR = ∠UST = 70° (Vertically opposite angles)
Now,∠RPQ = ∠QSR = 70°
Remember: Opposite angles of a parallelogram are equal.
∠LPR + ∠RPQ + ∠MPQ =180° (Linear pair of angles)
⇒35°+70°+∠MPQ=180°
⇒∠MPQ=180°−105°=75°