In the given figure, AB || CD and BC || ED. Find the value of x.

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)

$\Rightarrow x^{\circ}=105^{\circ}$

$\Rightarrow x=105$

 

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