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ehidna [41]
3 years ago
9

In the figure, ray OB bisects ∠TOY.

Mathematics
1 answer:
Levart [38]3 years ago
8 0

<u><em>Answer:</em></u>

∠BOY = 38°

<u><em>Explanation:</em></u>

<u>From the diagram, we can note that:</u>

m∠TOY = m∠TOB + m∠BOY ...................> equation I

We are given that ray OB bisects the angle

<u>Therefore:</u>

m∠TOB = m∠BOY

<u>Substitute in equation I:</u>

m∠TOY = m∠TOB + m∠TOB = 2m∠TOB ............> equation II

<u>We are given that:</u>

m∠TOY = 8x-36

m∠TOB = x+24

<u>Substitute with the givens in equation II and solve for x:</u>

m∠TOY = 2m∠TOB

8x - 36 = 2(x + 24)

2(4x-18) = 2(x+24)

4x - 18 = x + 24

3x = 42

x = 14

<u>This means that:</u>

m∠TOB = x + 24 = 14 + 24 = 38°

<u>Since </u>

m∠TOB = m∠BOY

<u>Therefore:</u>

m∠BOY = 38°

<u>Check:</u>

m∠TOY = 8x - 36 = 8(14) - 36 = 76° which is twice m∠TOB

Hope this helps :)

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