We are given a figure with two parallel lines $p$ and $q$, intersected by transversals $j, k, m, n$. We are given that $m\angle 1 = 50^\circ$ and $m\angle 3 = 60^\circ$. We are asked to find the measures of angles 4, 5, 2, 6, 7, and 8.

1. Problem Description

We are given a figure with two parallel lines $p$ and $q$, intersected by transversals $j, k, m, n$.

We are given that $m\angle 1 = 50^\circ$ and $m\angle 3 = 60^\circ$. We are asked to find the measures of angles 4, 5, 2, 6, 7, and

8.

2. Solution Steps

*Angle 4:*

$\angle 1$ and $\angle 4$ are corresponding angles. Since lines $p$ and $q$ are parallel, corresponding angles are congruent. Therefore, $m\angle 4 = m\angle 1 = 50^\circ$.

*Angle 5:*

$\angle 3$ and $\angle 5$ are corresponding angles. Since lines $p$ and $q$ are parallel, corresponding angles are congruent. Therefore, $m\angle 5 = m\angle 3 = 60^\circ$.

*Angle 2:*

$\angle 1$ and $\angle 2$ are supplementary angles, so $m\angle 1 + m\angle 2 = 180^\circ$.

$m\angle 2 = 180^\circ - m\angle 1 = 180^\circ - 50^\circ = 130^\circ$.

*Angle 6:*

Angles 4, 5, and 6 form a straight line, so their measures add up to $180^\circ$.

$m\angle 4 + m\angle 5 + m\angle 6 = 180^\circ$

$50^\circ + 60^\circ + m\angle 6 = 180^\circ$

$110^\circ + m\angle 6 = 180^\circ$

$m\angle 6 = 180^\circ - 110^\circ = 70^\circ$.

*Angle 7:*

$\angle 2$ and $\angle 7$ are corresponding angles. Since lines $p$ and $q$ are parallel, corresponding angles are congruent. Therefore, $m\angle 7 = m\angle 2 = 130^\circ$.

*Angle 8:*

$\angle 6$ and $\angle 8$ are corresponding angles. Since lines $p$ and $q$ are parallel, corresponding angles are congruent. Therefore, $m\angle 8 = m\angle 6 = 70^\circ$.

3. Final Answer

$m\angle 4 = 50^\circ$

$m\angle 5 = 60^\circ$

$m\angle 2 = 130^\circ$

$m\angle 6 = 70^\circ$

$m\angle 7 = 130^\circ$

$m\angle 8 = 70^\circ$