Question

In the given figure, ST is the diameter of the circle with center O, PQ is the tangent at point R. If ∠TRQ = 40°, find ∠RTS. 

(a) 40° 

(b) 50° 

(c) 60° 

(d) 30°

Answer 1

Answer : (b) 50º 

∠TSR = ∠TRQ = 40° (Angles in alternate segment are equal) 

ST being the diameter, ∠SRT = 90° (Angle in a semi-circle) 

∴ ∠RTS = 180° – (∠TSR + ∠SRT) 

= 180° – (130°) 

= 50°.