In the given figure, O is center of the circle and angle OBA = 50°. The angle P is :

1. 50°

2. 80°

3. 40°

4. 60°

From figure,

In △ OAB,

OA = OB (Radius of common circle)

We know that,

Angles opposite to equal sides of a triangle are equal.

∴ ∠A = ∠B = 50°

By angle sum property of triangle,

⇒ ∠A + ∠B + ∠O = 180°

⇒ 50° + 50° + ∠O = 180°

⇒ ∠O + 100° = 180°

⇒ ∠O = 180° - 100° = 80°.

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.

⇒ ∠O = 2∠P

⇒ ∠P = $\dfrac{∠O}{2} = \dfrac{80°}{2}$ = 40°.

Hence, Option 3 is the correct option.