First, from the diagram and the fact that lines m and n are parallel we get that:
1)
[tex]39^{\circ}+\measuredangle1=180^{\circ}.[/tex]
Therefore:
[tex]\measuredangle1=180^{\circ}-39^{\circ}=141^{\circ}.[/tex]
2) Angles 1 and 3 are opposed by the vertex, and the same occurs for angles 5 and 7, 4 and 6, and the angle of measure 39 degrees and 2, therefore:
[tex]\begin{gathered} \measuredangle1=\measuredangle3\text{ }\Rightarrow\measuredangle3=141^{\circ}, \\ \measuredangle2=39^{\circ}, \\ \measuredangle5=\measuredangle7, \\ \measuredangle4=\measuredangle6. \end{gathered}[/tex]
3) Angles 3 and 5 are alternate interior angles, and the same occurs for angles 2 and 4, therefore:
[tex]\begin{gathered} \measuredangle5=\measuredangle3=141^{\circ}, \\ \measuredangle4=\measuredangle2=39^{\circ}. \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} \measuredangle1=141^{\circ}, \\ \measuredangle2=39^{\circ}, \\ \measuredangle3=141^{\circ}, \\ \measuredangle4=39^{\circ}, \\ \measuredangle5=141^{\circ}, \\ \measuredangle6=39^{\circ}, \\ \measuredangle7=141^{\circ}. \end{gathered}[/tex]
