In the given figure, O is the centre of the circle and ∠OPQ = 30°. Then, ∠PAQ = ?

1. 60°

2. 70°

3. 80°

4. 75°

From figure,

OP = OQ (Radii of same circle)

∠OQP = ∠OPQ = 30° (As angles opposite to equal sides are equal)

In △POQ,

By angle sum property of triangle,

∠POQ + ∠OQP + ∠OPQ = 180°

∠POQ = 180° - ∠OQP - ∠OPQ

∠POQ = 180° - 30° - 30°

∠POQ = 120°.

We know that,

The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

∴ ∠POQ = 2∠PAQ

∴ ∠PAQ = $\dfrac{1}{2}$ ∠POQ

= $\dfrac{120^{\circ}}{2}$ = 60°.

Hence, option 1 is the correct option.