In the given figure, O is the centre of a circle. Then $∠ O A B = ?$

(a) $50^{\circ}$

(b) $60^{\circ}$

(c) $55^{\circ}$

(d) $65^{\circ}$

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Solution

ANSWER:
(d) 65°
We have:
OA = OB (Radii of a circle)
Let ∠ OAB = ∠ OBA = x °
In Δ OAB, we have:
x ° + x ° + 50° = 180° (Angle sum property of a triangle)
⇒ 2 x ° = (180° - 50°) = 130°
⇒ x=1302°=65°
Hence, ∠OAB = 65°

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