Question

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two parallel lines are cut by a transversal as shown below.
suppose $m\angle 2=96^\circ$. find $m\angle 5$ and $m\angle 7$.
$m\angle 5 = 96^\circ$
$m\angle 7 = 96^\circ$

Explanation:

Step1: Identify ∠2 and ∠5 relationship

∠2 and ∠5 are same-side interior angles. For parallel lines cut by a transversal, same-side interior angles are supplementary (sum to $180^\circ$).
$m\angle 5 = 180^\circ - m\angle 2$
$m\angle 5 = 180^\circ - 96^\circ = 84^\circ$

Step2: Identify ∠2 and ∠7 relationship

∠2 and ∠7 are alternate exterior angles. For parallel lines cut by a transversal, alternate exterior angles are congruent.
$m\angle 7 = m\angle 2 = 96^\circ$

Answer:

$m\angle 5 = 84^\circ$, $m\angle 7 = 96^\circ$