Question

Please help me find mBOC!
mZAOC = 96
mZBOC = 8x - 67
MZAOB = 9x - 75

Answer 1

`\bf Step-by-step~explanation:`

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.

`\bf Step~1:`

To solve for x: We set up our equation like this:

`\bf(9x-75)+(8x-67)=96`

Let's add the like terms together.

`\bf9x+8x=17x\\-75-67=-142`

`\bf Step~2:`

Our equation now:

`\bf 17x-142=96`

Now, we add 142 on both sides to get 17x on its own.

`\bf17x-142(+142)=96(+142)\\17x=238`

`\bf Step~3:`

Divide both sides by 17 to get our value for x.

`\bf(17x)/(17) =x\\\\(238)/(17)= 14\\\\x=14`

`\bf Step~4:`

Now that we have x's value, we plug it into the equation for m∠BOC.

`\bf 8x-67\\8(14)-67\\112-67\\45`

`\large\boxed{\bf Our~final~answer: mBOC=45}`