Question

solve for $x$. figures are not necessarily drawn to scale.
answer attempt 1 out of 2
$x = $

Explanation:

Step1: Identify similar triangles

Since \(\angle V=\angle S = 46^{\circ}\) and \(\angle VTU=\angle STR\) (vertically - opposite angles), \(\triangle VTU\sim\triangle STR\) by the AA (Angle - Angle) similarity criterion.

Step2: Use the property of similar triangles

For similar triangles \(\triangle VTU\) and \(\triangle STR\), the ratios of corresponding sides are equal. That is \(\frac{VT}{ST}=\frac{UT}{RT}=\frac{VU}{SR}\). We use \(\frac{UT}{RT}=\frac{VU}{SR}\). Substituting \(UT = 9\), \(RT=15\), \(SR = 20\) and \(VU=x\) into the proportion \(\frac{9}{15}=\frac{x}{20}\).
Cross - multiply: \(15x=9\times20\).

Step3: Solve for \(x\)

First, calculate \(9\times20 = 180\). Then the equation becomes \(15x=180\). Divide both sides by 15: \(x=\frac{180}{15}\).

Answer:

\(x = 12\)