1. **Problem:** Construct a rectangle in which one of the diagonals divides the angles into 30° and 60°. 2. **Understanding the problem:** In a rectangle, all angles are 90°. The diagonal divides the right angle into two parts: 30° and 60°. 3. **Key fact:** The diagonal of a rectangle splits the right angle into two angles whose sum is 90°, so if one is 30°, the other is 60°. 4. **Using trigonometry:** Let the rectangle have sides $a$ and $b$, and diagonal $d$. The diagonal forms two right triangles with angles 30° and 60°. 5. **From the triangle with angle 30°:** The side opposite 30° is half the hypotenuse. So if the diagonal $d$ is the hypotenuse, then the side opposite 30° is $\frac{d}{2}$. 6. **Assign sides:** Let side $a$ be opposite 30°, so $a = \frac{d}{2}$. 7. **Side $b$ opposite 60°:** Using the relation $b = a \sqrt{3}$, so $b = \frac{d}{2} \sqrt{3}$. 8. **Conclusion:** The rectangle sides are in ratio $1 : \sqrt{3}$, and the diagonal length $d$ can be any positive number. **Final answer:** A rectangle with sides $a$ and $b$ such that $a = \frac{d}{2}$ and $b = \frac{d}{2} \sqrt{3}$, where $d$ is the diagonal length.