Question

two parallel lines are cut by a transversal as shown below.
suppose ( m angle 3 = 84 ^ { circ } ). find ( m angle 6 ) and ( m angle 8 ).

Explanation:

Step1: Use the property of alternate interior angles

Alternate interior angles are equal when two parallel lines are cut by a transversal. $\angle3$ and $\angle6$ are alternate interior angles. So, $m\angle6 = m\angle3$.
Since $m\angle3 = 84^{\circ}$, then $m\angle6=84^{\circ}$.

Step2: Use the property of corresponding angles

Corresponding angles are equal when two parallel lines are cut by a transversal. $\angle3$ and $\angle8$ are corresponding angles. So, $m\angle8 = m\angle3$.
Since $m\angle3 = 84^{\circ}$, then $m\angle8 = 84^{\circ}$.

Answer:

$m\angle6 = 84^{\circ}$
$m\angle8 = 84^{\circ}$