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Condition for Two Lines to Be Parallel

Question

For what value of $x$ will $l_{1}$ and $l_{2}$ be parallel lines

$32^{\circ}$
None of these
$42^{\circ}$
$12^{\circ}$

A

32^{\circ}

B

None of these

C

12^{\circ}

D

42^{\circ}

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Solution

Verified by Toppr

We know when two parallel lines are cut by any transversal, then the sum of two consecutive interior angles is $180^{o}$ .
Here $(2 x^{o})$ and $(3 x + 20^{o})$ are consecutive interior angles.
So,
$(2 x^{o}) + (3 x + 20^{o}) = 180^{o}$
$=> 180^{o} - 20^{o} = 3 x + 2 x$
$=> 5 x = 160^{o}$
So, $x = 32^{o}$
$∴$ for $x = 32^{o}$ $l_{1}$ and $l_{2}$ will be parallel lines

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