Question

two parallel lines are cut by a transversal as shown below.
suppose $m\angle 6=56^{\circ}$. find $m\angle 1$ and $m\angle 4$.
$m\angle 1=\square^{\circ}$
$m\angle 4=\square^{\circ}$

Explanation:

Step1: Find $m\angle1$ (corresponding angles)

Corresponding angles of parallel lines are equal, so $m\angle1 = m\angle6$.
$m\angle1 = 56^\circ$

Step2: Find $m\angle4$ (supplementary to $\angle1$)

$\angle1$ and $\angle4$ are supplementary (linear pair), so $m\angle4 = 180^\circ - m\angle1$.
$m\angle4 = 180^\circ - 56^\circ = 124^\circ$

Answer:

$m\angle1 = 56^\circ$
$m\angle4 = 124^\circ$