In the given figure, if TP and TQ are tangents to a circle with centre O, so that ∠ POQ = 110°, then ∠PTQ is

It is given that ∠ POQ = 110°

Since, the tangent at any point of a circle is perpendicular to the radius through the point of contact,

∠ OPT = 90° and ∠ OQT = 90°

Now, in quadrilateral POQT,

∠ POQ + ∠ OQT + ∠ PTQ + ∠ OPT = 360°

⇒ 110° + 90° + ∠ PTQ + 90° = 360°

⇒ ∠ PTQ = 70°