Question:
In the given figure, AB || CD and BC || ED. Find the value of x.
Solution:
$B C \| E D$ and $\mathrm{CD}$ is the transversal.
Then,
$\angle B C D+\angle C D E=180^{\circ} \quad$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow \angle B C D+75=180$
$\Rightarrow \angle B C D=105^{\circ}$
$A B \| C D$ and $\mathrm{BC}$ is the transversal.
$\angle A B C=\angle B C D$ (alternate angles)
$\Rightarrow x^{\circ}=105^{\circ}$
$\Rightarrow x=105$