Question

In the given figure, a tangent has been drawn at a point P on the circle centred at O.

If ∠TPQ = 110°, then ∠POQ is equal to:

Options

• 110°

• 70°

• 140°

• 55°

Answer 1

140°

Explanation:

In a circle, the angle between the tangent and the chord through the point of contact equals the angle in the alternate segment. Therefore, if ∠TPQ = 110°, ∠POQ is the exterior angle of the ΔPOQ, which is twice the angle subtended by the chord PQ at the circumference.

∠POQ = 2 × (180° − 110°)

= 2 × 70°

= 140°