AP and AQ are two tangents drawn to a circle with center O from an external point A. If ∠PAQ = 40°, then ∠POQ is:

Correct option is D

Given:

To a circle with center at O, two tangents AP and AQ are drawn from an external point A.

∠PAQ = 40°

Concept:

Tangent of a circle is perpendicular to radius.

Solution: 

PAQ + ∠OPA + ∠OQA + ∠POQ = 360

=> 40° + 90° + 90° + ∠POQ = 360°

=> ∠POQ = 360° - 220°

=> ∠POQ = 140°

∴  The value of ∠POQ is 140°.