Question

For what value of $x$ will ${l_1}$ and ${l_2}$ be parallel lines and why?

Answer 1

Hint: Use the property, “If two parallel lines are cut by any transversal, then the sum of two consecutive interior angles is ${180^\circ }$” to find the value of $x$.

Complete step-by-step answer:
Here ${l_1}\parallel {l_2}$ and a transversal $t$ cut both the lines.
We know that when two parallel lines are cut by any transversal, then the sum of two consecutive interior angles is ${180^\circ }$.
Here $2{x^\circ }$ and ${\left( {3x + 20} \right)^\circ }$ are consecutive interior angles.
So, $2{x^\circ } + {\left( {3x + 20} \right)^\circ } = {180^\circ }$
$ \Rightarrow $$5x + {20^\circ } = {180^\circ }$
$ \Rightarrow $$5x = {180^\circ } - {20^\circ }$
$ \Rightarrow $$5x = {160^\circ }$
$ \Rightarrow $$x = \dfrac{{{{160}^\circ }}}{5}$
$ \Rightarrow $$x = {32^\circ }$

$\therefore $For $x = {32^\circ }$, ${l_1}$ and ${l_2}$ be parallel lines.

Note: For checking that two lines are parallel or not, any one of the conditions mentioned below is to be satisfied:
If two lines are cut by a transversal such that the pair of corresponding angles are equal to each other, then the pair of lines are parallel.
If two lines are cut by a transversal such that the sum of interior angles on the same side of the transversal is ${180^\circ }$, then the pair of lines are parallel.
If two lines are cut by a transversal such that the pair of alternate interior angles are equal to each other, then the pair of lines are parallel.