Step 1
When two parallel lines are cut by a transversal, corresponding angles and vertically opposite angles are formed.
Given:
[tex]\begin{gathered} m\angle3=59^o \\ \end{gathered}[/tex]
Required: To find
[tex]m\angle6\text{ and m}\angle8[/tex]
Step 2
Find the value of the required
[tex]\begin{gathered} m\angle3=m\angle1=59^o(vertically\text{ opposite angles are equal)} \\ m\angle2=180\text{ - m}\angle3(Sum\text{ of angles on straight line is 180)} \\ m\angle2=180-59=121^o \end{gathered}[/tex][tex]\begin{gathered} m\angle2=m\angle6(corresponding\text{ angles are equal}) \\ m\angle6=121^o \end{gathered}[/tex][tex]\begin{gathered} m\angle6=m\angle8(vertically\text{ opposite are equal)} \\ m\angle8=121^o \end{gathered}[/tex]
Hence,
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