Question

solve for ( x ). round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
answer attempt 1 out of 2
( x = )

Explanation:

Step1: Identify similar triangles

Since \(\angle W = \angle Z=88^{\circ}\), \(\angle V=\angle Y = 38^{\circ}\), and \(\angle U=\angle X=54^{\circ}\), \(\triangle WUV\sim\triangle ZXY\) (by AAA similarity criterion).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{WU}{ZX}=\frac{WV}{ZY}\). Substituting the known values: \(\frac{6}{x}=\frac{10}{30}\).

Step3: Solve for \(x\)

Cross - multiply: \(10x = 6\times30\). Then \(10x=180\). Divide both sides by 10: \(x=\frac{180}{10}=18\).

Answer:

\(x = 18\)