Question

two parallel lines are cut by a transversal as shown below. suppose m∠4 = 77°. find m∠6 and m∠7.

Explanation:

Step1: Identify angle - relationship

$\angle4$ and $\angle6$ are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary, i.e., $m\angle4 + m\angle6=180^{\circ}$.

Step2: Calculate $m\angle6$

Given $m\angle4 = 77^{\circ}$, then $m\angle6=180^{\circ}-m\angle4$. So $m\angle6 = 180 - 77=103^{\circ}$.

Step3: Identify angle - relationship for $\angle7$

$\angle4$ and $\angle7$ are alternate exterior angles. When two parallel lines are cut by a transversal, alternate exterior angles are congruent. So $m\angle7=m\angle4$.

Step4: Determine $m\angle7$

Since $m\angle4 = 77^{\circ}$, then $m\angle7 = 77^{\circ}$.

Answer:

$m\angle6 = 103^{\circ}$
$m\angle7 = 77^{\circ}$