1. **Problem statement:** Given trapezoid-like figure with $TU \parallel VX$, and lengths $UV=15$, $TW=12$, and $TU=25$, find the length $WX$. 2. **Key concept:** When two lines are parallel, corresponding sides in similar triangles are proportional. 3. **Set up proportion:** Since $TU \parallel VX$, triangles $TUV$ and $VWX$ are similar. 4. **Write the proportion:** $$\frac{TU}{VX} = \frac{UV}{WX}$$ 5. **Plug in known values:** $$\frac{25}{VX} = \frac{15}{WX}$$ 6. **We need to find $WX$, but $VX$ is unknown. However, $VX$ is the segment from $V$ to $X$, and $WX$ is the segment from $W$ to $X$. Since $TW=12$, and $WX$ is unknown, we can use the fact that $VX = TW + WX = 12 + WX$. 7. **Rewrite proportion with $VX = 12 + WX$: $$\frac{25}{12 + WX} = \frac{15}{WX}$$ 8. **Cross multiply:** $$25 \times WX = 15 \times (12 + WX)$$ 9. **Expand right side:** $$25WX = 180 + 15WX$$ 10. **Subtract $15WX$ from both sides:** $$25WX - 15WX = 180$$ 11. **Simplify:** $$10WX = 180$$ 12. **Divide both sides by 10:** $$\cancel{10}WX = \frac{180}{\cancel{10}}$$ 13. **Final value:** $$WX = 18$$ **Answer:** The length $WX$ is 18.