Question

In Fig., line l || m and n is a transversal. If ∠1 = 40°, find all the angles and check that all corresponding angles and alternate angles are equal.

Answer 1

In the given figure, l || m.
Here,
$$\begin{gathered} \angle 1+\angle 2=180°\left(\mathrm{Linear}\mathrm{pair}\right) \\ \therefore \angle 2=180°-\angle 1=180°-40°=140° \\ \angle 5=\angle 1=40°\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle 3=\angle 1=40°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \\ \angle 7=\angle 3=40°\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle 7=\angle 5=40°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \end{gathered}$$
Also,
$$\begin{gathered} \angle 2=\angle 6=140°\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle 2=\angle 4=140°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \\ \angle 4=\angle 8=140°\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle 8=\angle 6=40°\left(\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}\right) \end{gathered}$$
Thus,
$\angle 2=\angle 8,\angle 3=\angle 5,\angle 6=\angle 4,\angle 1=\angle 7$
Hence, alternate angles are equal.