Question

uv || tw. find wx.
wx =

Explanation:

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

Since \( \overline{UV}\parallel\overline{TW}\), we have \(\frac{WX}{VX}=\frac{TX}{UX}\). Let \(WX = x\), then \(VX=x + 15\), \(TX = 50\), and \(UX=50 + 25=75\). So, \(\frac{x}{x + 15}=\frac{50}{75}\).

Step2: Cross - multiply the proportion

Cross - multiplying gives \(75x=50(x + 15)\).
Expanding the right - hand side: \(75x=50x+750\).

Step3: Solve for \(x\)

Subtract \(50x\) from both sides: \(75x-50x=50x + 750-50x\).
\(25x=750\).
Divide both sides by \(25\): \(x=\frac{750}{25}=30\).

Answer:

\(30\)