Respuesta :

Answer:

45°

Step-by-step explanation:

From the diagram :

  • ∠AOC = ∠AOB + ∠BOC
  • 96 = 9x - 75 + 8x - 67
  • 17x - 142 = 96
  • 17x = 238
  • x = 238/17
  • x = 14

Finding ∠BOC :

  • ∠BOC = 8x - 67
  • ∠BOC = 8(14) - 67
  • ∠BOC = 112 - 67
  • ∠BOC = 45°
falyassiri82

Answer:

Alrighty... i am happy that you would like an explanation.. that is truly admirable...

let's begin!!!

Step-by-step explanation:

We need to place everything into an equation to solve for x... after that we can substitute the value for x into the expression for m<BOC to get its value (i hope this isn't confusing... the math is easier though... trust me)

8X -67 +9X -75 = 96              Add 67 and 75 to both sides to isolate x

8X +9X = 238       --> 17X = 238

divide both sides by 17 to get x = 14

then subsitute x = 14 into the expression for m < BOC

you get  8(14)-67 = 45

therefore, the measure of <BOC is 45 degrees

I really hope this helps!!!!!