<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 :)
<h3>
Answer: PC = 5</h3>
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Work Shown:
AB+BC+CD = AD .... segment addition postulate
BC+BC+CD = AD ... replace AB with BC (since AB = BC)
BC+BC+BC = AD ... replace CD with BC (since BC = BC)
3*BC = AD .... combine like terms
3*BC = 12 .... replace AD with 12
BC = 12/3 .... divide both sides by 3
BC = 4
For right triangle PBC, the legs are BP = 3 and BC = 4. We can use the Pythagorean Theorem to find that the hypotenuse is PC = 5
The steps are shown below
(BP)^2+(BC)^2 = (PC)^2
3^2+4^2 = (PC)^2
9+16 = (PC)^2
25 = (PC)^2
(PC)^2 = 25
PC = sqrt(25)
PC = 5
The other parts of the diagram seem to be thrown in as a distraction.
2+2=4 2 X 2 = 4 2 X 3 = 6
4,6,8 are being counted by twos so the next one is 10
4•3= 12, 6+3=9, 8-3=6, the next operation I assume would be division so 10/3= 3.34
