Answer:
∠BOY = 38°
Explanation:
From the diagram, we can note that:
m∠TOY = m∠TOB + m∠BOY ...................> equation I
We are given that ray OB bisects the angle
Therefore:
m∠TOB = m∠BOY
Substitute in equation I:
m∠TOY = m∠TOB + m∠TOB = 2m∠TOB ............> equation II
We are given that:
m∠TOY = 8x-36
m∠TOB = x+24
Substitute with the givens in equation II and solve for x:
m∠TOY = 2m∠TOB
8x - 36 = 2(x + 24)
2(4x-18) = 2(x+24)
4x - 18 = x + 24
3x = 42
x = 14
This means that:
m∠TOB = x + 24 = 14 + 24 = 38°
Since
m∠TOB = m∠BOY
Therefore:
m∠BOY = 38°
Check:
m∠TOY = 8x - 36 = 8(14) - 36 = 76° which is twice m∠TOB
Hope this helps :)
