Question

what is the value of x?
enter your answer in the box.
□ cm

Explanation:

Step1: Identify the theorem

This is a case of the Angle Bisector Theorem, which states that if a bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. So, $\frac{VY}{YK}=\frac{VT}{TK}$.

Step2: Substitute the known values

We know $VY = 34$, $YK = x$, $VT = 95.2$, and $TK = 168$. Substituting into the proportion: $\frac{34}{x}=\frac{95.2}{168}$.

Step3: Cross - multiply and solve for x

Cross - multiplying gives $95.2x=34\times168$. First, calculate $34\times168 = 5712$. Then, $x=\frac{5712}{95.2}$.

Step4: Perform the division

$\frac{5712}{95.2}=60$.

Answer:

60