Question

vz || wy. find xz.
xz =

Explanation:

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

Since \(\overline{VZ}\parallel\overline{WY}\), we have \(\frac{XY}{XZ}=\frac{XW}{XV}\). Let \(XZ = x\), then \(XY=x - 18\), \(XW=36 - 24=12\), and \(XV = 36\).
So, \(\frac{x - 18}{x}=\frac{12}{36}\)

Step2: Simplify the equation

Cross - multiply: \(36(x - 18)=12x\)
Expand: \(36x-648 = 12x\)
Subtract \(12x\) from both sides: \(36x-12x-648=0\)
\(24x=648\)
Divide both sides by \(24\): \(x=\frac{648}{24}=27\)

Answer:

\(27\)