Question

In the figure, if l||m||n and $\angle 1={60}^0$, find $\angle 2$.

Answer 1

In the figure, l||m||n and a transversal p, intersects them at P, Q and R respectively
$\angle 1={60}^0$
$\therefore \angle 1=\angle 3$ (Corresponding angles)
$\therefore \angle 3=\angle {60}^0$
But $\angle 3+\angle 4={180}^0$ (Linear pair)
${60}^0+\angle 4={180}^0\Rightarrow \angle 4={180}^0-{60}^0$
$\therefore \angle 4={120}^0$
But $\angle 2=\angle 4$ (Alternate angles)
$\therefore \angle 2={120}^0$