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ray ZP bisects ∠OZQ so that ∠OZP = 8x – 9 and ∠PZQ = 5x + 18. Find the value of x, and the measure of each angle. You must show all work in order to receive credit!

ray ZP bisects OZQ so that OZP 8x 9 and PZQ 5x 18 Find the value of x and the measure of each angle You must show all work in order to receive credit class=

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mreijepatmat
Since ZP is the bisector of ∠ OZQ, then we can say:

∠OZP = ∠PZQ

8x-9 = 5x+18 
8x-5x = 18 + 9
3x = 27  
x= 27/3 → x = 9

Now plugin the value of x in both angles:
a) 8x - 9 = 8(9) -9 and " 8x - 9 = 63°
b) 5x +18 = 5(9) + 18 and "5x+18" =63°


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