Notice that the angle 2 and that of 135º are vertical angles. Since vertical angles are congruent, they have the same measure. Then:
[tex]m\angle2=135º[/tex]Notice that the angles 2 and 4 are alternate interior angles. Alternate interior angles are congruent. Then, the measure of 4 is the same as the measure of 2:
[tex]m\angle4=135º[/tex]The angles 3 and 4 are adjacent and form a straight line. Therefore, those angles are supplementary angles, then, their measures must add up to 180º:
[tex]m\angle4+m\angle3=180[/tex]Since the measure of the angle 4 is 135º, then:
[tex]\begin{gathered} 135+m\angle3=180 \\ \Rightarrow m\angle3=180-135 \\ \therefore m\angle3=45 \end{gathered}[/tex]Finally, notice that the angles 3 and 5 are also vertical angles, so they have the same measure:
[tex]m\angle5=45º[/tex]Therefore, the answers are:
[tex]\begin{gathered} m\angle2=135º \\ m\angle3=45º \\ m\angle4=135º \\ m\angle5=45º \end{gathered}[/tex]