Find the value of x for which the line AB will become parallel to line CD.

$7^{\circ}$

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$10^{\circ}$

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$9^{\circ}$

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$12^{\circ}$

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Solution

The correct option is D
$12^{\circ}$

The line AB will become parallel to line CD, if
$∠ A F G + ∠ C G F = 180^{\circ}$
i.e. Co. interior angles are supplementary
$∴$ $84^{\circ} + 9 x - 12^{\circ} = 180^{\circ} 9 x + 72^{\circ} = 180^{\circ} 9 x = 108^{\circ} x = 12^{\circ}$

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