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