Angle 2 and angle of 34° are vertical angles, then they are congruent, that is,
[tex]m\angle2=34\degree[/tex]
Angle 6 and angle of 34° are corresponding angles, then they are congruent, that is,
[tex]m\angle6=34\degree[/tex]
Angle 4 and angle of 34° are alternate interior angles, then they are congruent, that is,
[tex]m\angle4=34\degree[/tex]
Angle 7 and angle of 34° are same-side interior angles, then they are supplementary, that is,
[tex]\begin{gathered} m\angle7+34\degree=180\degree \\ m\angle7=180\degree-34\degree \\ m\angle7=146\degree \end{gathered}[/tex]
Angles 4 and 3 are same-side interior angles, then they are supplementary, that is,
[tex]\begin{gathered} m\angle4+m\angle3=180\degree \\ 34\degree+m\angle3=180\degree \\ m\angle3=180\degree-34\degree \\ m\angle3=146\degree \end{gathered}[/tex]
Angles 7 and 5 are vertical angles, then they are congruent, that is,
[tex]\begin{gathered} m\angle5=m\angle7 \\ m\angle5=146\degree \end{gathered}[/tex]
Angles 1 and 3 are vertical angles, then they are congruent, that is,
[tex]\begin{gathered} m\angle1=m\angle3 \\ m\angle1=146\degree \end{gathered}[/tex]
