1. **State the problem:** We are given that $\angle SQR \cong \angle STU$ and need to solve for $x$, where $x$ is the length of segment $SU$. The segments are: $SU = x$, $UR = 8.6$, $ST = 17.1$, and $TQ = 12.9$. 2. **Identify the triangles and use the Angle-Angle (AA) similarity criterion:** Since $\angle SQR \cong \angle STU$ and they share $\angle S$, triangles $SQR$ and $STU$ are similar. 3. **Set up the proportion of corresponding sides:** $$\frac{SU}{ST} = \frac{UR}{TQ}$$ Substitute known values: $$\frac{x}{17.1} = \frac{8.6}{12.9}$$ 4. **Solve for $x$:** Multiply both sides by 17.1: $$x = 17.1 \times \frac{8.6}{12.9}$$ Calculate the fraction: $$\frac{8.6}{12.9} \approx 0.6667$$ Then: $$x \approx 17.1 \times 0.6667 = 11.4$$ 5. **Final answer:** $$\boxed{11.4}$$ Thus, $x \approx 11.4$ to the nearest tenth.