Question

inthe given figure boa is a diameter of a circle and the tangent at a point p meets ba extended at t of angle pbo os 30 degree then find angle pta

Answer 1

angle p=90..as ab is the diameter.therefore angle pab= 60.... angle tap will be 180 -. 60 as tab is a straight line...angle tpa will be 30 (exterior opposite) therefore the third angle will be 30 therefore angle PTA will be 30

Answer 2

join OP and radius is same 
∠OPB=30
∠POB=120......sum of triangle
∠POT=60...linear pair
∠TPO=90
then,∠PTO=30.....sum of triangle property
30 is answer.