O is the center of circle angle PSQ=30 degree find angle APQ

Angle QPS=90^o [Angle in a semi-circle=90^o
                                              OR
                             Angle subtended by diameter on the circumference of a circle=90^o]
90^o+30^o+Angle PQS=180^o [Angle sum property of triangle]
Angle PQS=180^o-120^o=60^o
Join OP. [Construction]
OQ=OP [radius]
Angle OQP=Angle OPQ=60^o [Angle opposite to equal sides are equal]
Angle APO=90^o [radius is perpendicular to the tangent at the point of contact]
60^o+Angle APQ=90^o
Angle APQ=90^o-60^o=30^o
Hope it helps!