In the given figure, O is the centre of the circle. Find the value of $X$ .

$30^{\circ}$

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$40^{\circ}$

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$50^{\circ}$

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$100^{\circ}$

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Solution

The correct option is C
$50^{\circ}$

In the figure, $∠ A B D = 50^{\circ}$

Since the angles subtended by an arc in the same segment are equal, we have $∠ A B D = ∠ A C D .$

$\Rightarrow X = ∠ A C D = 50^{\circ}$

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