In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P.

We know that a chord passing through the centre is the diameter of the circle.
∵∠QPR = 90∘    (Angle in a semi circle is 90∘)
By using alternate segment theorem
We have ∠APQ = ∠PRQ = 58∘
Now, In △PQR
∠PQR + ∠PRQ + ∠QPR = 1800            [Angle sum property of a triangle]
⇒ ∠PQR + 58∘ +  900 = 180∘                      
⇒ ∠PQR= 32∘
Hence, the correct answer is option (a).