In the figure, ray ob bisects ∠toy.
if m∠toy = 8x - 36 and m∠tob = x + 24, what is m∠boy?
a) 14°
b) 38°
c) 76°
d) 112°

∠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 :)

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