Answer :
As we know that the angle opposite to equal sides are equal.
∴ ∠1 = ∠2 ……(1)
Sum of all the angles of a triangle is 180°.
In Δ PAB,
∠1 + ∠2 + ∠APB = 180°
⇒ ∠1 + ∠2 + 50° = 180° (given ∠APB = 50°)
⇒ ∠1 + ∠2 = 130°
⇒ ∠1 + ∠1 = 130° (From equation 1)
⇒ 2∠1 = 130°
⇒ ∠1 = 65° ….(2)
We know that the angle between the tangent and radius is 90° .
∴ ∠1 + ∠OAB = 90°
⇒ 65° + ∠OAB = 90° (From equation 2)
⇒ ∠OAB = 25°
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