Question

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

Options

• 50°

• 80°

• 40°

• 60°

Answer 1

In the given figure, O is centre of the circle and angle OBA = 50°.
The angle P is 40°.

Explanation: 

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 = `(∠O)/2` = `(80°)/2`= 40°.