In the figure, ray ob bisects ∠toy.
if m∠toy = 8x - 36 and m∠tob = x + 24, what is m∠boy?

Step-by-step explanation:

Look at the picture.

If OB is bisects of ∠TOY, then

m∠TOB = m∠BOY ⇒ m∠TOY = m∠TOB + m∠BOY ⇒ m∠TOY = 2m∠TOB.

We have

m∠TOY = 8x - 36, and m∠TOB = x + 24.

Substitute:

8x - 36 = 2(x + 24)       divdie both sides by 2

4x - 18 = x + 24         add 18 to both sides

4x = x + 42            subtract x from both sides

3x = 42             divide both sides by 3

x = 14

m∠BOY = m∠TOB = x + 24

Put x = 14:

m∠BOY = 14 + 24 = 38

the answer is 37

step-by-step explanation: