1. **State the problem:** We have two triangles, a large triangle WZY and a smaller triangle WVX inside it. Given that $\overline{YZ} \parallel \overline{VX}$, we need to find the length of $WX$. 2. **Identify the given lengths:** - $WZ = 28$ - $ZY = 14$ - $XY = 15$ 3. **Use the property of parallel lines in triangles:** When a segment is drawn parallel to one side of a triangle, it creates a smaller triangle similar to the original triangle. Here, $VX \parallel YZ$ implies $\triangle WVX \sim \triangle WZY$. 4. **Set up the similarity ratios:** Corresponding sides of similar triangles are proportional: $$\frac{WX}{WZ} = \frac{VX}{ZY} = \frac{WV}{WZ + ZY}$$ Since $VX \parallel YZ$, the ratio of sides is: $$\frac{WX}{WZ} = \frac{VX}{ZY}$$ 5. **Find the length of $WX$:** We know $XY = 15$ and $ZY = 14$, but $XY$ is part of the larger triangle's base, so we consider the total base $WY = WZ + ZY = 28 + 14 = 42$. Since $VX \parallel YZ$, the smaller triangle's base $WX$ corresponds to $WZ$ in the larger triangle, and the segment $XY$ corresponds to $ZY$. 6. **Calculate the ratio:** $$\frac{WX}{28} = \frac{15}{14}$$ 7. **Solve for $WX$:** $$WX = 28 \times \frac{15}{14}$$ 8. **Simplify:** $$WX = \cancel{28}^2 \times \frac{15}{\cancel{14}^7} = 2 \times 15 = 30$$ **Final answer:** $$WX = 30$$