Question

In the given figure, O is the centre of O the circle. AB is the tangent to the circle at the point P. If ∠APQ = 58° then the measure of ∠PQB is ______.

Options

• 32°

• 58°

• 122°

• 132°

Answer 1

In the given figure, O is the centre of O the circle. AB is the tangent to the circle at the point P. If ∠APQ = 58° then the measure of ∠PQB is 32°.

Explanation:

∠QPR = 90°   ...[Angle in a semicircle]

And ∠QRP = ∠APQ = 58°   ...[Angles in alternate segments]

In ΔPQR, we have ∠PQR + ∠QRP + ∠QPR = 180° 

⇒ ∠PQR = 32°

∴ ∠PQB = ∠PQR = 32°.