Question

find wx.
wx =
submit

Explanation:

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

Since \(ZY\parallel YW\), we have \(\frac{ZY}{ZX}=\frac{VW}{VX}\). Also, \(ZX = 35\), \(ZY=14\), and \(VX = 75\). Let \(WX=x\), then \(VW = 75 - x\).
So, \(\frac{14}{35}=\frac{75 - x}{75}\).

Step2: Simplify the proportion

Simplify \(\frac{14}{35}\) to \(\frac{2}{5}\). The equation becomes \(\frac{2}{5}=\frac{75 - x}{75}\).
Cross - multiply: \(2\times75=5\times(75 - x)\).
Which is \(150 = 375-5x\).

Step3: Solve for \(x\)

Add \(5x\) to both sides: \(150 + 5x=375\).
Subtract \(150\) from both sides: \(5x=375 - 150=225\).
Divide both sides by \(5\): \(x = 45\).

Answer:

\(45\)