Question

In the adjoining figure, it is being given that AO || CD, OB || CE and ∠AOB = 50°
Find the measure of ∠ECD.

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{AO}\parallel \mathrm{CD} \\ \mathrm{OB}\parallel \mathrm{CE} \\ \angle \mathrm{AOB}=50° \\ \angle \mathrm{AOD}=\angle \mathrm{CDB}=50°(\mathrm{when}\mathrm{AO}\parallel \mathrm{CD}\mathrm{and}\mathrm{OB}\mathrm{is}\mathrm{the}\mathrm{transversal}) \\ \angle \mathrm{ECD}+\angle \mathrm{CDB}=180°(\mathrm{consecutive}\mathrm{interior}\mathrm{angles}\mathrm{are}\mathrm{supplementary},\mathrm{DB}\parallel \mathrm{CE}\mathrm{and}CD\mathrm{is}the\mathrm{transversal}) \\ \angle \mathrm{ECD}=180°-50°=130° \end{gathered}$$