# In the given figures below, decide whether $l$ is parallel to $m$."

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To do:

We have to decide whether $l$ is parallel to $m$ in each case.

Solution:

We know that,

The sum of interior angles on the same side of transversal is $180^o$.

(i) Here,

Sum of the interior angles on the same side of the line $n=126^{\circ}+44^{\circ}$

$=170^{\circ}$

$≠180^{\circ}$

Therefore, $l$ is not parallel to $m$.

(ii) Let the angle opposite to $75^{\circ}$ be $x$.

$x=75^{\circ}$                      [Vertically opposite angles]

Sum of interior angles on the same side of the line $n=x+75^{\circ}$

$=75^{\circ}+75^{\circ}$

$=150^{\circ}$

$≠180^{\circ}$

Therefore, $l$ is not parallel to $m$.

(iii) Let the angle opposite to $57^{\circ}$ be $y$

Therefore, $y=57^{\circ}$             [Vertically opposite angles]

Sum of interior angles on the same side of the line $n=57^{\circ}+123^{\circ}$

$= 180^{\circ}$

Therefore, $l$ is parallel to $m$.

(iv) Let the angle opposite to $72^{\circ}$ be $z$.

Therefore $z=72^{\circ}$               [Vertically opposite angles]

$=72^{\circ}$

Sum of interior angles on the same side of the line $n=z+98^{\circ}$

$=72^{\circ}+98^{\circ}$

$=170^{\circ}$

$≠180^{\circ}$

Therefore, $l$ is not parallel to $m$.

Updated on 10-Oct-2022 13:34:00