1. **State the problem:** We need to construct a rectangle where one diagonal divides the opposite angles into 50 degrees and 40 degrees. 2. **Recall properties of a rectangle:** All angles in a rectangle are 90 degrees. 3. **Analyze the diagonal's effect:** The diagonal divides a 90-degree angle into two parts: 50 degrees and 40 degrees, which sum to 90 degrees, consistent with the rectangle's angle. 4. **Use triangle properties:** Consider the triangle formed by the diagonal and two adjacent sides. The diagonal acts as the hypotenuse. 5. **Label the rectangle ABCD with diagonal AC:** Angle at A is split into 50° and 40° by diagonal AC. 6. **Calculate the length ratio of sides:** Using the triangle with angles 50°, 40°, and 90°, the sides opposite these angles relate by sine ratios. 7. **Let side AB = a and side AD = b:** Then, by sine rule in triangle ABC, $$\frac{a}{\sin 40^\circ} = \frac{b}{\sin 50^\circ}$$ 8. **Express ratio:** $$\frac{a}{b} = \frac{\sin 40^\circ}{\sin 50^\circ}$$ 9. **Calculate approximate values:** $$\sin 40^\circ \approx 0.6428, \quad \sin 50^\circ \approx 0.7660$$ 10. **Ratio:** $$\frac{a}{b} \approx \frac{0.6428}{0.7660} \approx 0.839$$ 11. **Conclusion:** To construct such a rectangle, choose sides so that the ratio of side AB to side AD is approximately 0.839. This ensures the diagonal divides the opposite angles into 50° and 40° as required.