Question

In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If $\angle$ APQ = ${58}^o$ then the measure of $\angle$ PQB is

(a) ${32}^o$ (b) ${58}^o$ (c) ${122}^o$ (d) ${132}^o$

Answer 1

We know that, <APO = 90° (As AB is the tangent)

Thus
<QPO = 90° - 58° = 32°

Now, in triangle OPQ, OP = OQ (radii of the circle)
Therefore <QPO = <OQP = 32°
Thus <PQB = <OQP = 32°

(a) 32° is correct answer