Question

solve for $x$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
answer attempt 2 out of 2
$x = 12.2$ submit answer

Explanation:

Step1: Find the third angle of triangle \( \triangle STU \)

The sum of angles in a triangle is \( 180^{\circ} \). Let the third angle of \( \triangle STU \) be \( \angle U \). Then \( \angle U=180^{\circ}-(63^{\circ} + 72^{\circ})=45^{\circ} \)

Step2: Prove the similarity of triangles

In \( \triangle STU \) and \( \triangle V W X \), \( \angle S=\angle V = 63^{\circ}\), \( \angle U=\angle X = 45^{\circ}\). By the AA (angle - angle) similarity criterion, \( \triangle STU\sim\triangle V W X \)

Step3: Set up the proportion using the similarity of triangles

Since the triangles are similar, the ratios of their corresponding sides are equal. That is \( \frac{ST}{VX}=\frac{SU}{VW}\)
We know \( ST = 13\), \( SU = 17\), \( VW=16\), and \( VX=x\)
Substituting the values into the proportion: \( \frac{13}{x}=\frac{17}{16}\)

Step4: Solve for \( x \)

Cross - multiply: \( 17x=13\times16\)
\( 17x = 208\)
\( x=\frac{208}{17}\approx12.2\)

Answer:

\( x = 12.2\)