Question
In the given figure, decide whether $l$ is parallel to $m.$
✓
Answer
In the above figure we see that, angle $x$ and $75^{\circ}$ are forming a linear pair on the line $I$
Therefore,
$x+75^{\circ}=180^{\circ} \text { (Sum of angles of linear pair) }$
$x=180^{\circ}-75^{\circ}=105^{\circ}$
For the lines $I$ and m to be parallel, Corresponding angles, $\angle \mathrm{ABC}$ and $\angle \mathrm{x}$ should be equal
But, $\angle \mathrm{x}=105^{\circ}$
And, $\angle A B C=75^{\circ}$
Therefore, Lines $I$ and $m$ are not parallel to each other.
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