Question

In the figure 1.83 measure of some angles are given . Which two lines are parallel and which two are not. Justify.

Answer 1

From the figure, we can observe that

$$\begin{gathered} \angle 1+105°=180°(\mathrm{Linear}\mathrm{pair}) \\ \Rightarrow \angle 1=75°....\left(\mathrm{i}\right) \\ \mathrm{The}\mathrm{corresponding}\mathrm{angles}\mathrm{are}\mathrm{equal}. \\ \therefore l\parallel m \\ \mathrm{However},\angle 1\ne \angle 2=65° \\ \mathrm{i}.\mathrm{e}.,\mathrm{the}\mathrm{corresponding}\mathrm{angles}\mathrm{are}\mathrm{not}\mathrm{equal}. \\ \therefore m\nparallel n\mathrm{and}l\nparallel n \end{gathered}$$