In the given figure, CO = OD & ∠OCD=30∘. Find ∠AOB? [3 MARKS]

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In the given figure, CO = OD & $∠ O C D = 30^{\circ}$ . Find $∠ A O B$ ? [3 MARKS]

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Answer: Option A
:

Concept: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Sum of the angles of a triangle is $180^{\circ}$ .
Since OC = OD, $∠ O C D = ∠ O D C = 30^{\circ}$
[Angles opposite to equal sides are equal]
$\Rightarrow ∠ C O D = 180^{\circ} - (30^{\circ} + 30^{\circ}) = 120^{\circ}$
$∠ A O B = ∠ C O D$ [Vertically Opposite Angles]
$∴ ∠ A O B = 120^{\circ}$

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