Question

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

Answer 1

$EF\parallel CD$ and CE is the transversal.
Then,
$$\begin{gathered} \angle ECD+\angle CEF=180°\left[\text{Consecutive Interior Angles}\right] \\ \Rightarrow \angle ECD+130°=180° \\ \Rightarrow \angle ECD=50° \end{gathered}$$
Again, $AB\parallel CD$ and BC is the transversal.
Then,
$$\begin{gathered} \angle ABC=\angle BCD\left[\text{Alternate Interior Angles}\right] \\ \Rightarrow 70°=x+50°\left[\because \angle BCD=\angle BCE+\angle ECD\right] \\ \Rightarrow x=\mathbf{20}\mathbf{°} \end{gathered}$$