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In the following figure AB and CD are parallel to each other, find the value of $x$ .

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90^{\circ}

100^{\circ}

120^{\circ}

140^{\circ}

answer is B.

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Detailed Solution

Given figure is,
Question Image

Now draw a line parallel to

AB

and

CD

and passing through

E

as shown in the figure
which divides

x

∠ L_{1}

and

∠ L_{2}

Now,

AB | | EF

and

BE

is transversal.

∴ ∠ L_{1} + 120^{\circ} = 180^{\circ}

(sum of angles made on side of transversal is supplementary)

\Rightarrow ∠ L_{1} = 180^{\circ} - 120^{\circ}

\Rightarrow ∠ L_{1} = 60^{\circ}

Also

DC | | EF

and

DE

is transversal.

∴ ∠ L_{2} + 140^{\circ} = 180^{\circ}

(sum of angles made on side of transversal is supplementary)

\Rightarrow ∠ L_{2} = 180^{\circ} - 140^{\circ}

\Rightarrow ∠ L_{1} = 40^{\circ}

And,

x = ∠ L_{1} + ∠ L_{2}

\Rightarrow x = 60^{\circ} + 40^{\circ}

\Rightarrow x

= 100^{\circ}

Hence, the correct option is 2.

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