Question

In fig 2.57, if AB || DE $\angle$BAC = 35$°$ and $\angle$CDE = 53$°$, find $\angle$DCE.

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{AB}\parallel \mathrm{DE} \\ \mathrm{Also},\angle \mathrm{BAC}=\angle \mathrm{CED}=35°(\mathrm{Alternate}\mathrm{angles}) \\ \mathrm{In}△\mathrm{DCE},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{DCE}+\angle \mathrm{CDE}+\angle \mathrm{CED}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow \angle \mathrm{DCE}+53°+35°=180° \\ \Rightarrow \angle \mathrm{DCE}=92° \end{gathered}$$