In the given figure, O is the centre of the circle, and $∠ O A B = 20 °$ and $∠ O C B = 50 °$ . Find $∠ A O C$ .

60°

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70°

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50°

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20°

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Solution

The correct option is A 60°
$O A = O C$ (radii of the same circle)
$∠ O A B = ∠ O B A = 20 °$
In $O A B$ ,
$∠ O A B + ∠ A O B + ∠ B O A = 180 °$
$20 ° + 20 ° + ∠ B O A = 180 °$
$∠ B O A = 140 °$
$O B = O C$ (radii of the same circle)
$∠ O B C = ∠ O C B = 50 °$
In $O C B$ ,
$∠ O B C + ∠ O C B + ∠ C O B = 180 °$
$50 ° + 50 ° + ∠ C O B = 180 °$
$∠ C O B = 80 °$
$∠ A O B = ∠ A O C + ∠ B O C$
$∠ A O C = ∠ A O B - ∠ B O C$
$∠ A O C = 140 ° - 80 °$
$∠ A O C = 60 °$

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Similar questions

∠ O A B = 20^{\circ}

∠ O C B = 50^{\circ}

∠ A O C

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) $60^{\circ}$

∠ O A B = 30^{\circ}

∠ O C B = 55^{\circ}

∠ B O C

∠ A O C

∠ O A B = 20^{\circ}, ∠ O C B = 55^{\circ}

∠ B O C

∠ A O C

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