The question gives us the following parameters:
[tex]\begin{gathered} m\angle4=105\degree \\ m\angle6=50\degree \end{gathered}[/tex]Recall that the sum of angles on a straight line is 180 degrees. This means that:
[tex]\begin{gathered} m\angle3+m\angle4=180\degree \\ \therefore \\ m\angle3=180-m\angle4=180-105 \\ m\angle3=75\degree \end{gathered}[/tex]Recall that the sum of angles in a triangle is 180 degrees. Thus, we have:
[tex]\begin{gathered} m\angle2+m\angle3+m\angle6=180\degree \\ \therefore \\ m\angle2=180-m\angle3-m\angle6=180-75-50 \\ m\angle2=55\degree \end{gathered}[/tex]The SECOND OPTION is correct.