Answer : (c) ∠z
∠QSR = ∠QTR = \(\frac{1}{2}\) ×∠QOR = \(\frac{z}{2}\)
(Angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle)
∠PSM = ∠PTM = 180º - \(\frac{z}{2}\) (Straight line)
Also, ∠SMT = ∠QMR = y (vert. opp. ∠s)
∴ In quad. PSMT, ∠SMT + ∠PTM + ∠TPS + ∠PSM = 360°
⇒ y + 180° – \(\frac{z}{2}\) + x + 180° – \(\frac{z}{2}\) = 360°
⇒ x + y = z.