We are given a diagram with lines $j$, $k$, $m$, $n$, $p$, and $q$. We know that $m\angle 1 = 50^\circ$ and $m\angle 3 = 60^\circ$. Lines $p$ and $q$ are parallel. We need to find the measures of $\angle 4$, $\angle 5$, $\angle 2$, $\angle 6$, $\angle 7$, and $\angle 8$.

1. Problem Description

We are given a diagram with lines $j$, $k$, $m$, $n$, $p$, and $q$. We know that $m\angle 1 = 50^\circ$ and $m\angle 3 = 60^\circ$. Lines $p$ and $q$ are parallel. We need to find the measures of $\angle 4$, $\angle 5$, $\angle 2$, $\angle 6$, $\angle 7$, and $\angle 8$.

2. Solution Steps

Since lines $p$ and $q$ are parallel, we can use properties of angles formed by transversals.

2

6. $\angle 4$ is supplementary to $\angle 1$, so $m\angle 4 + m\angle 1 = 180^\circ$. Therefore, $m\angle 4 = 180^\circ - m\angle 1 = 180^\circ - 50^\circ = 130^\circ$.

2

7. $\angle 5$ is supplementary to $\angle 3$, so $m\angle 5 + m\angle 3 = 180^\circ$. Therefore, $m\angle 5 = 180^\circ - m\angle 3 = 180^\circ - 60^\circ = 120^\circ$.

2

8. $\angle 2$ and $\angle 4$ are vertical angles, so $m\angle 2 = m\angle 4 = 130^\circ$.

2

9. $\angle 6$ and $\angle 3$ are corresponding angles, so $m\angle 6 = m\angle 3 = 60^\circ$.

3

0. $\angle 7$ is supplementary to $\angle 2$, so $m\angle 7 + m\angle 2 = 180^\circ$. Therefore, $m\angle 7 = 180^\circ - m\angle 2 = 180^\circ - 130^\circ = 50^\circ$.

3

1. $\angle 8$ and $\angle 1$ are corresponding angles, so $m\angle 8 = m\angle 1 = 50^\circ$.

3. Final Answer

2

6. $m\angle 4 = 130^\circ$

2

7. $m\angle 5 = 120^\circ$

2

8. $m\angle 2 = 130^\circ$

2

9. $m\angle 6 = 60^\circ$

3

0. $m\angle 7 = 50^\circ$

3

1. $m\angle 8 = 50^\circ$