Question

In the given figure, AB || CD, ∠ECD = 100°, ∠EAB = 50° and ∠AEC = x°. Find the value of x.
Figure

Answer 1

Draw $EF\parallel AB\parallel CD$.
Now, $EF\parallel AB\text{and}EA$ is the transversal.
$$\begin{gathered} \therefore \angle EAB+\angle AEF=180°\left[\text{Sum of consecutive interior angles is supplementary}\right] \\ \Rightarrow 50°+\angle AEF=180° \\ \Rightarrow \angle AEF=180°-50°=130° \end{gathered}$$
Also,
$EF\parallel CD\text{and}EC$ is the transversal.
$$\begin{gathered} \therefore \angle ECD+\angle CEF=180°\left[\text{Sum of consecutive interior angles is supplementary}\right] \\ \Rightarrow 100°+\angle CEF=180° \\ \Rightarrow \angle CEF=80° \end{gathered}$$
Now,
$$\begin{gathered} \angle AEC+\angle CEF=\angle AEF \\ \Rightarrow x°+80°=130° \\ \Rightarrow x°=130°-80°=50° \\ \mathrm{Therefore},x=50 \end{gathered}$$