Answer: 98 millimeters
Explanation:
Since angle VTY is congruent to angle VTK, segment TY bisects angle VTK. Since Y is on segment VK, between V and K, we can use the Angle Bisector Theorem, which states that
[tex] \frac{VY}{YK} = \frac{VT}{TK} [/tex] (1)
Since x= VK = VY + YK, we need to obtain VY since YK = 68.
VY is obtained by multiplying the denominator YK on both sides of equation (1). So,
[tex]VY = \frac{(VY)(VT)}{TK} = \frac{(68)(57)}{129.2} \newline VY = 30[/tex]
Hence,
x = VK = VY + YK
x = 30 + 68
x = 98 millimeters
