From the diagram given we notice that angle 2 and angle 4 are vertical opposite angles, which means that the are equal, that is:
[tex]m\angle2=m\angle4[/tex]
and hence we have that:
[tex]m\angle4=128[/tex]
We also notice that angles 4 and 5 are consecutive interior angles, and since the lines are parallel this means that they have to add to 180°:
[tex]m\angle4+m\angle5=180[/tex]
Plugging the value of angle 4 and solving for angle 5 we have:
[tex]\begin{gathered} 128+m\angle5=180 \\ m\angle5=180-128 \\ m\angle5=52 \end{gathered}[/tex]
Finally, we notice that angles 5 and 7 are vertically opposite which means they are equal, hence:
[tex]m\angle7=52[/tex]
Therefore, we conclude that:
[tex]\begin{gathered} m\angle5=52 \\ m\angle7=52 \end{gathered}[/tex]
