Question

In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ∠1, ∠2 and ∠3.

Answer 1

According to the given figure,
m || n and are cut by transversal p.
$\angle 2=120°(\mathrm{alternate}\mathrm{interior}\mathrm{angles}\mathrm{are}\mathrm{equal})$
Also, l || m. So, $\angle 1=\angle 3(\mathrm{corresponding}\mathrm{angles})$
Also, $\angle 3\mathrm{and}120°\mathrm{form}\mathrm{a}\mathrm{linear}\mathrm{pair}.$
$$\begin{gathered} \angle 3+120°=180° \\ \Rightarrow \angle 3=180-120 \\ \Rightarrow \angle 3=60° \end{gathered}$$

And $\angle 1=\angle 3=60°,\angle 2=120°$