Question

vw || ux. find tu.
tu =

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

Since \( \overline{VW}\parallel\overline{UX} \), we have the proportion \( \frac{TX}{XW}=\frac{TU}{UV} \). Let \( TU = x \). Then \( TX=75 - 50=25 \), \( XW = 50 \), and \( UV = 32 \). The proportion becomes \( \frac{25}{50}=\frac{x}{32} \).

Step2: Solve the proportion for \( x \)

Cross - multiply: \( 50x=25\times32 \). So \( 50x = 800 \). Then \( x=\frac{800}{50}=16 \).

Answer:

\(16\)