Part A
In parallel lines, because of the symmetry, some angles are equal.
In the following image we see in the same color the angles that are equal or congruent:
The yellow angles are equal, and the red angles are equal.
In this case, we are asked for the relationship between angles 1 and 8.
Angles 1 and 8 are alternate exterior angles.
Part B
Since alternate exterior angles are equal, we have for the values given in part B that:
[tex]\begin{gathered} m\angle1=m\angle8 \\ (3x+50)=(5x-20) \end{gathered}[/tex]
Part C
We need to find m∠2.
For that, first, we need to find the value of x by solving the equation from part B:
[tex]\begin{gathered} (3x+50)=(5x-20) \\ 3x+50=5x-20 \\ 50+20=5x-3x \\ 70=2x \\ \frac{70}{2}=x \\ 35=x \end{gathered}[/tex]
Since x is equal to 35, angle 1 is equal to:
[tex]\begin{gathered} m\angle1=3x+50 \\ m\angle1=3(35)+50 \\ m\angle1=155 \end{gathered}[/tex]
And in the image, we can see that angles 1 and 2 are supplementary angles: the sum of them is 180°:
[tex]\begin{gathered} m\angle1+m\angle2=180 \\ \text{substituting m}\angle1=155 \\ 155+m\angle2=180 \\ \text{Subtracting 155 to both sides:} \\ m\angle2=180-155 \\ m\angle2=25 \end{gathered}[/tex]
m∠2=25
