Question
In the given figure, decide whether $l$ is parallel to $m.$
✓
Answer
In the above figure we see that, Angle $x$ and $123^{\circ}$ are forming a linear pair on the line $m$
Therefore,
$x+123^{\circ}=180^{\circ} \text { (Sum of angles of linear pair) }$
$\Rightarrow x=180^{\circ}-123^{\circ}=57^{\circ}$
We have to show that I and $m$ are parallel to each other.
For this, Corresponding angles $\angle \mathrm{ABC}$ and $\angle \mathrm{x}$ should be equal
Now, $\angle \mathrm{x}=57^{\circ}$
And, $\angle A B C=57^{\circ}$
Therefore, Both the angles are equal to each other
Hence, Lines $I$ and $m$ are parallel to each other.
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