Given data:
The given figure.
The expression for the angle AOC is,
[tex]\angle AOC=\angle\text{AOB}+\angle BOC[/tex]Substitute the given values in the abbove expression.
[tex]\begin{gathered} 96^{\circ}=(9x-75^{\circ})+(8x-67^{\circ}) \\ 238^{\circ}=17x \\ x=14 \end{gathered}[/tex]Substitute 14 for x in the angle BOC.
[tex]\begin{gathered} \angle BOC=(8(14)-67)^{\circ} \\ =45^{\circ} \end{gathered}[/tex]