Question

uy || vx. find wy. wy =

Explanation:

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

Since \( \overline{UY}\parallel\overline{VX}\), we have \(\frac{WV}{VU}=\frac{WX}{XY}\). Let \(WY = x\), then \(XY=x - 36\) and \(WV = 20\), \(VU = 10\).

Step2: Set up the proportion equation

\(\frac{20}{10}=\frac{36}{x - 36}\). Cross - multiply gives \(20(x - 36)=10\times36\).

Step3: Expand and solve the equation

Expand: \(20x-720 = 360\). Add \(720\) to both sides: \(20x=360 + 720\). So \(20x = 1080\). Divide both sides by \(20\): \(x=\frac{1080}{20}=54\).

Answer:

\(54\)