Question

In the given figure, $AB\parallel CD\parallel EF$. Find the value of x ?

Answer 1

It is given that $AB\parallel CD$ and $BC$ is transversal

from the figure we know that $\angle BCD$ and $\angle ABC$ are alternate interior angles

so we get

$\angle ABC=\angle BCD$

in order to find the value of $x$ we can write it as

$x^o+\angle ECD={70}^o....\left(i\right)$

It is given that $CD\parallel EF$ and $CE$ is transversal

from the figure we know that $\angle ECD$ and $\angle CEF$ are consecutive interior angles

so we get

$\angle ECD+\angle CEF={180}^o$

by substituting the values

$\angle ECD+{130}^o={180}^o$

$\angle ECD={180}^o-{130}^o$

$\angle ECD={50}^o$

Now by substituting $\angle ECD$ in equation (i) we get

$x^o+\angle ECD={70}^o$

$x^o+{50}^o={70}^o$

$x^o={20}^o$

therfore the value of $x$ is ${20}^o$