Question

At what angle must a transversal cut two parallel lines, such that all the angles thus formed in the system are equal?

Answer 1

Consider the following figure where lines l and m are parallel and is cut by a transversal n.

For all angles to be equal:
$\angle 1=\angle 2-----------\left(i\right)\mathrm{Also},\angle 1+\angle 2=180°\Rightarrow 2\angle 1=180°\Rightarrow \angle 1=90°\Rightarrow \angle 2=90°$

Subsequently, all angles are equal to 90°.
Therefore the transversal must be perpendicular to the pair of parallel lines.