Question
In the given figure, $AB\ ||\ CD$. Find the value of $x$.
✓
Answer
Since $AB\ ||\ CD$ and $BC$ is a transversal.
So, $\angle\text{BCD}=\angle\text{ABC}=\text{x}^\circ$ [Alternate angles]
As $BC\ ||\ ED$ and $CD$ is a transversal.
$\angle\text{BCD}+\angle\text{EDC}=180^\circ$
$\Rightarrow\angle\text{BCD}+75^\circ=180^\circ$
$\Rightarrow\angle\text{BCD}=180^\circ-75^\circ=105^\circ$
$\Rightarrow\angle\text{ABC}=105^\circ$ $[$ Since $\angle\text{BCD}=\angle\text{ABC}]$
$\therefore\text{x}^\circ=\angle\text{ABC}=105^\circ$
Hence, $\text{x}=105.$
So, $\angle\text{BCD}=\angle\text{ABC}=\text{x}^\circ$ [Alternate angles]
As $BC\ ||\ ED$ and $CD$ is a transversal.
$\angle\text{BCD}+\angle\text{EDC}=180^\circ$
$\Rightarrow\angle\text{BCD}+75^\circ=180^\circ$
$\Rightarrow\angle\text{BCD}=180^\circ-75^\circ=105^\circ$
$\Rightarrow\angle\text{ABC}=105^\circ$ $[$ Since $\angle\text{BCD}=\angle\text{ABC}]$
$\therefore\text{x}^\circ=\angle\text{ABC}=105^\circ$
Hence, $\text{x}=105.$
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