[tex]\bf Step-by-step~explanation:[/tex]
We are given that m∠AOC is 96º. One angle's expression is 8x - 67 and the other is 9x - 75. That means when we add both of these angles, they would equal to 96º.
[tex]\bf Step~1:[/tex]
To solve for x: We set up our equation like this:
[tex]\bf(9x-75)+(8x-67)=96[/tex]
Let's add the like terms together.
[tex]\bf9x+8x=17x\\-75-67=-142[/tex]
[tex]\bf Step~2:[/tex]
Our equation now:
[tex]\bf 17x-142=96[/tex]
Now, we add 142 on both sides to get 17x on its own.
[tex]\bf17x-142(+142)=96(+142)\\17x=238[/tex]
[tex]\bf Step~3:[/tex]
Divide both sides by 17 to get our value for x.
[tex]\bf\frac{17x}{17} =x\\\\\frac{238}{17}= 14\\\\x=14[/tex]
[tex]\bf Step~4:[/tex]
Now that we have x's value, we plug it into the equation for m∠BOC.
[tex]\bf 8x-67\\8(14)-67\\112-67\\45[/tex]
[tex]\large\boxed{\bf Our~final~answer: mBOC=45}[/tex]
