29. Exemplar exercise problems IV

1. In figure, if \(O\) is the centre of a circle, \(PQ\) is a chord and the tangent \(PT\) at \(P\) makes an angle of \(50^\circ\) with \(PQ\) then \(\angle POQ\) is equal to

 

2. In figure, if \(PA\) and \(PB\) are tangents to the circle with centre \(O\) such that \(\angle APB = 50^\circ\) , then \(\angle OAB\) is equal to