Question

In a o center circle Pq is a tangent q I joined by a st line to o . Pr is diameter. S a point on tangent qp . s and r are joined T is a point on lying on the circference and it also lies on st line sr if LPSR IS 75 ° then find Lpqo and Lqts

Answer 1

OPR=90( radius is always perpendicular to tangent) 
RPQ+QPO=90
QPO=90-50
QPO=40
OP=OQ (radii) 
OPQ=OQP=40(angles opp to equal sides) 
In triangle OPQ
OPQ+OQP+POQ=180(ASP)
POQ=180-80
POQ=100