In the given figure, AP and BP are tangents to a circle with centre O. If ∠APB = 62° then the measure of ∠AQB is:

59°

In quadrilateral AOBP ,

∠PAO + ∠PBO + ∠AOB + ∠APB = 360º

90º + 90º + ∠AOB + 62º = 360º

∠AOB = 118º

We know that by same arc angle made at center is double to the angle made at circumference.

∠AQB = \(\frac{∠AOB}{2}\)

= \(\frac{ 118º}{2}\)

= 59º