Constructible Angles
To determine which angles can be constructed using a ruler and compass, we must refer to the properties of constructible angles. An angle is constructible if it can be formed using these tools, typically if it can be expressed in terms of 30-degree increments.

Criteria for Constructibility
- **Constructible Angles**: An angle θ is constructible if the cosine of θ can be expressed as a solution of a polynomial equation with rational coefficients. In simpler terms, the angle can be derived from a series of constructions starting from the basic angles of 0°, 30°, 45°, and 60°.
- **Rational Angles**: The angles that can be constructed are typically of the form \( \frac{360}{2^n} \) degrees, where n is a non-negative integer (like 0, 1, 2, etc.). Also, angles formed by adding or subtracting these constructible angles are also constructible.

Analysis of Options
- **a) 400°**: This angle is equivalent to 40° (as it can be reduced by subtracting 360°), which is not a constructible angle since it cannot be expressed as a combination of 30° increments.
- **b) 37.50°**: This angle can be constructed. It can be derived as follows:
- 37.5° = 30° + 7.5°
- 7.5° = 15° / 2, and 15° is a constructible angle (15° = 30° / 2).
- **c) 650°**: This simplifies to 290° (650° - 360°), which is also not constructible based on the aforementioned criteria.
- **d) 500°**: This simplifies to 140°, which also cannot be formed using the basic constructible angles.

Conclusion
Thus, among the options provided, only **37.5°** is constructible using a ruler and compass, making option **b** the correct answer.