Question

In the given figure, PT touches the circle whose center is O, at R. Diameter SQ when produced meets PT at P. If ∠SPR = x°, ∠QRP = y°, then x + 2y =

(a) 100° 

(b) 120° 

(c) 80° 

(d) 90°

Answer 1

Answer : (d) 90º 

 ∠QSR = ∠QRP = y° (Angles in alternate segment are equal) 

Also, ∠QRS = 90° (Angle in a semi-circle) 

∠PRS = ∠PRQ + ∠QRS = y° + 90° 

In ∆ PRS, ∠SPR + ∠PRS + ∠PSR = 180° 

⇒ x° + y° + 90° + y° = 180° 

⇒ x + 2y = 90°.