Answer:
m∠BOY = 38
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
