solve for x. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Answer:

$x = 52.1$

Explanation:

Step1: Identify similar - triangles

The two triangles $\triangle FGH$ and $\triangle IJK$ have the same angle measures ($45^{\circ}$, $104^{\circ}$, $31^{\circ}$), so they are similar.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. We can set up the proportion $\frac{FG}{IJ}=\frac{HG}{KJ}$. Substituting the given values: $\frac{23}{x}=\frac{32}{72}$.

Step3: Cross - multiply

Cross - multiplying gives us $32x=23\times72$.

Step4: Calculate the right - hand side

$23\times72 = 1656$, so $32x = 1656$.

Step5: Solve for $x$

$x=\frac{1656}{32}=51.75\approx52.1$.