Question

two parallel lines are cut by a transversal as shown below. suppose m∠4 = 103°. find m∠6 and m∠7.

Explanation:

Step1: Identify angle - pair relationships

$\angle4$ and $\angle6$ are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So $m\angle6=m\angle4$.

Step2: Determine the measure of $\angle6$

Since $m\angle4 = 103^{\circ}$, then $m\angle6=103^{\circ}$.

Step3: Identify the relationship between $\angle4$ and $\angle7$

$\angle4$ and $\angle7$ are same - side exterior angles. When two parallel lines are cut by a transversal, same - side exterior angles are supplementary, that is $m\angle4 + m\angle7=180^{\circ}$.

Step4: Calculate the measure of $\angle7$

$m\angle7=180^{\circ}-m\angle4$. Substitute $m\angle4 = 103^{\circ}$ into the equation, we get $m\angle7=180 - 103=77^{\circ}$.

Answer:

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