Find $ \mathrm{x} $ if $ \mathrm{AB}\|\mathrm{CD}\| \mathrm{EF} $."

Given:

$AB \parallel CD \parallel EF$.

To do:

We have to find the value of $x$.

Solution:

Let $\angle ECD=y$

$CD \parallel EF$ and $CE$ is the transversal.

This implies,

$\angle ECD$ and $\angle CEF$ are consecutive interior angles.

$\angle ECD+\angle CEF=180^o$ 

$y+140^o=180^o$

$y=180^o-140^o$

$y=40^o$

$AB \parallel CD$ and $BC$ is the transversal.

This implies,

$\angle BCD$ and $\angle ABC$ are alternate interior angles.

$\angle ABC=\angle BCD$

$60^o=x+y$

$60^o=x+40^o$

$x=60^o-40^o$

$x=20^o$

The value of $x$ is $20^o$.

Tutorialspoint

Updated on: 10-Oct-2022

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