1. **State the problem:** We have two triangles ABC and EFD with given sides and angles. We want to find the length $x = ED$ in triangle EFD. 2. **Identify the triangles:** Both triangles have the same angles: 47°, 58°, and 75°, so they are similar triangles by the Angle-Angle (AA) similarity criterion. 3. **Use similarity ratios:** Corresponding sides of similar triangles are proportional. The sides correspond as follows: - $AB$ corresponds to $ED$ - $BC$ corresponds to $EF$ - $AC$ corresponds to $DF$ (not given) 4. **Set up the proportion:** Using the sides we know, $$\frac{AB}{ED} = \frac{BC}{EF}$$ Substitute the known values: $$\frac{9}{x} = \frac{10}{20}$$ 5. **Solve for $x$:** Cross-multiply: $$9 \times 20 = 10 \times x$$ $$180 = 10x$$ Divide both sides by 10: $$\cancel{10}x = \frac{180}{\cancel{10}}$$ $$x = 18$$ 6. **Answer:** The length $ED$ is 18. This is the exact value, no rounding needed.