Given:
Angles E and F are given supplementary angles.
[tex]\begin{gathered} m\angle E=(9x-38)^{\circ} \\ m\angle F=(2x+42)^{\circ} \end{gathered}[/tex]
The supplementary angles are the angles whose measures add upto 180 degrees.
Hence,
[tex]m\angle E+m\angle F=180[/tex]
Substituting the values,
[tex]\begin{gathered} 9x-38+2x+42=180 \\ 11x+4=180 \\ 11x=180-4 \\ 11x=176 \\ x=\frac{176}{11} \\ x=16 \end{gathered}[/tex]
Hence,
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