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!

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°

Use pythagorean’s theorem and find the missing side lengths of the two smaller triangles and add them together
13^2 - 12^2 = 5
15^2 - 12^2 = 9
5+9 = 14
14 is the length of each side of the square
14^2 + 14^2 = 19.8
19.8 is the diagonal length of the inside if the square