Question

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two parallel lines are cut by a transversal as shown below.
suppose $m\angle 6=56^\circ$. find $m\angle 1$ and $m\angle 4$.
$m\angle 1 = 56^\circ$
$m\angle 4 = 124^\circ$

Explanation:

Step1: Find $m\angle 1$

$\angle 1$ and $\angle 6$ are corresponding angles. For parallel lines cut by a transversal, corresponding angles are congruent.
$m\angle 1 = m\angle 6 = 56^\circ$

Step2: Find $m\angle 4$

$\angle 4$ and $\angle 1$ are supplementary (they form a linear pair).
$m\angle 4 = 180^\circ - m\angle 1 = 180^\circ - 56^\circ = 124^\circ$

Answer:

$m\angle 1 = 56^\circ$
$m\angle 4 = 124^\circ$