Question

two parallel lines are cut by a transversal as shown below.
suppose $m\angle 8=142^{\circ}$. find $m\angle 2$ and $m\angle 3$.
$m\angle 2 = 142^{\circ}$
$m\angle 3 = \square^{\circ}$

Explanation:

Step1: Identify vertical angle of ∠8

$\angle 6 = m\angle 8 = 142^\circ$

Step2: Find ∠3 via corresponding angles

$\angle 3 = m\angle 6 = 142^\circ$
(Alternatively, use supplementary angle rule: $\angle 3 = 180^\circ - (180^\circ - 142^\circ) = 142^\circ$)

Answer:

$m\angle 2 = 142^\circ$
$m\angle 3 = 142^\circ$