Question

given lines ( l ), ( m ), and ( n ) are parallel and cut by two transversal lines, find the value of ( x ). round your answer to the nearest tenth if necessary.

Explanation:

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

Since \( l\parallel m\parallel n\), we have the proportion \(\frac{10}{x}=\frac{9}{40}\) (by the theorem of parallel lines cut by transversals).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(9x = 10\times40\). So, \(9x=400\).

Step3: Solve for \(x\)

Then \(x=\frac{400}{9}\approx44.4\)

Answer:

\(x\approx44.4\)