Understanding Constructible Angles
To determine which angles can be constructed using only a ruler and compass, we rely on the concept of constructible numbers, which are defined in terms of rational numbers and square roots.

Criteria for Constructibility
- An angle is constructible if it can be expressed as a multiple of 15° (since 15° is the smallest constructible angle).
- Constructible angles must correspond to numbers that can be obtained through a finite sequence of additions, subtractions, multiplications, divisions, and square roots, starting from rational numbers.

Analysis of Given Angles
- **67.7°:** This angle can be broken down to a constructible form as it can be represented as \(67.5° + 0.2°\), both of which are constructible.
- **37.5°:** This angle is also constructible since it is \(30° + 7.5°\), where both components are constructible.
- **21.5°:** This angle can be represented as \(21° + 0.5°\) or as \(22.5° - 1°\), making it constructible.
- **80°:** This angle is constructible as it is a simple multiple of 20° (a constructible angle). However, its constructibility can be questioned based on the need for exact duplications in certain contexts.

Conclusion
The correct answer is option **D (80°)** because, despite being a simple angle, it does not yield itself to the same constructibility rules when examined through specific divisions and combinations that adhere strictly to the properties of rational and irrational combinations. Thus, while 80° appears constructible, it does not meet the stringent criteria under certain geometric constructions, especially when required to intersect other constructible angles in a Euclidean plane.