Question

In each of the given figures, two lines l and m are cut by a transevrsal t.
Find whether l || m.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\angle 1+\angle 2=180(\mathrm{linear}\mathrm{pair}) \\ \mathrm{or}{130}^{°}+\angle 2=180° \\ \mathrm{or}\angle 2=50°\ne 40°=\angle 3 \\ \therefore \mathrm{l}\nparallel \mathrm{m} \\ \left(\mathrm{ii}\right)\angle 2+\angle 3=180°(\mathrm{linear}\mathrm{pair}) \\ 35°+\angle 3=180° \\ \angle 3=145°=145°=\angle 1 \\ \therefore \mathrm{l}\parallel \mathrm{m} \\ \left(\mathrm{iii}\right)\angle 2+\angle 3=180(\mathrm{linear}\mathrm{pair}) \\ \angle 3=180°-125°=55° \\ \angle 3=55°\ne 60°=\angle 1 \\ \therefore \mathrm{l}\nparallel \mathrm{m} \end{gathered}$$