In the given figure, AB || CD || EF. Find the value of x.

Question:

In the given figure, AB || CD || EF. Find the value of x.

Solution:

$E F \| C D$ and $\mathrm{CE}$ is the transversal

Then

$\angle E C D+\angle C E F=180^{\circ} \quad$ [Consecutive Interior Angles]

$\Rightarrow \angle E C D+130^{\circ}=180^{\circ}$

$\Rightarrow \angle F C D=50^{\circ}$

Again, $A B \| C D$ and $\mathrm{BC}$ is the transversal.

Then,

$\angle A B C=\angle B C D \quad[$ Alternate Interior Angles $]$

$\Rightarrow 70^{\circ}=x+50^{\circ} \quad[\because \angle B C D=\angle B C E+\angle E C D]$

$\Rightarrow x=20^{\circ}$

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