What is the value of x? triangle v t k with segment t y such that y is on segment v k, between v and k. angle v t y is congruent to angle y t k. v t equals 57 millimeters, v k equals x, y k equals 68 millimeters, and t k equals 129.2 millimeters.

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

    (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, 



Hence,

x = VK = VY + YK
x = 30 + 68
x = 98 millimeters