Segment TX bisects angle T
So the "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.
So according to the angle bisector theorem in triangle VTK,
[tex] \frac{VT}{TK} = \frac{VY}{YK} [/tex]
[tex] \frac{95.2}{168} = \frac{34}{YK} [/tex]
cross multiply
[tex] 95.2\times (YK) = 168 \times 34 [/tex]
[tex] 95.2\times (YK) [/tex] = 5712
To find YK, divide both side by 95.2
[tex] \frac{95.2\times (YK) }{95.2} = \frac{5712}{95.2} [/tex]
YK = 60
VK = x = VY + YK
x = 34 + 60
x = 94 cm
