In the given figure, O is the centre of a circle. Then, ∠OAB = ?
(a) 50°
(b) 60°
(c) 55°
(d) 65°

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Solution

(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)
⇒ 2x° = (180° - 50°) = 130°
⇒ $x = (\frac{130}{2}) ° = 65 °$
Hence, ∠OAB = 65°

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Similar questions

In the given figure, $O$ is the center of a circle in which $∠ O A B = 20^{\circ}$ and $∠ O C B = 50^{\circ} .$ Then, $∠ A O C =$ ?

(a) $50^{\circ}$
(b) $70^{\circ}$
(c) $20^{\circ}$
(d) $60^{\circ}$

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

(a) $50^{\circ}$

(b) $60^{\circ}$

(d) $65^{\circ}$

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