Question

In Fig., if AB || CD and CD || EF, find ∠ACE.

Answer 1

In the given figure, AB || CD and CD || EF.
Extend line CE to E^'.

Thus, we have:
$$\begin{gathered} \angle \mathrm{BAC}=\angle \mathrm{ACD}=70°\left(\mathrm{Alternate}\mathrm{angles}\right) \\ \mathrm{Now}, \\ \angle 3+\angle \mathrm{CEF}=180°\left(\mathrm{Linear}\mathrm{pair}\right) \\ \Rightarrow \angle 3=180°-\angle \mathrm{CEF}=180°-130°=50° \\ \mathrm{Since}\mathrm{CD}\left|\right|\mathrm{EF},\mathrm{then} \\ \angle 2=\angle 3=50°\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle \mathrm{ACE}=\angle \mathrm{ACD}-\angle 2=70°-50°=20° \end{gathered}$$