Question

vw || ux. find tw.
tw =

Explanation:

Step1: Find the length of \( VU \)

Since \( VT = 77 \) and \( UT = 35 \), then \( VU=VT - UT \).
\( VU = 77-35=42 \)

Step2: Use the Basic Proportionality Theorem (Thales' theorem)

Because \( \overline{VW}\parallel\overline{UX} \), we have \( \frac{TU}{VU}=\frac{TX}{WX} \). Let \( TW=x \), then \( TX=x - 30 \).
Substituting the values: \( \frac{35}{42}=\frac{x - 30}{30} \)
Cross - multiply: \( 35\times30=42\times(x - 30) \)
\( 1050 = 42x-1260 \)
Add \( 1260 \) to both sides: \( 1050 + 1260=42x \)
\( 2310=42x \)
Divide both sides by \( 42 \): \( x=\frac{2310}{42}=55 \)

Answer:

\( TW = 55 \)