The angles x - 10° and 190° - x are: A. interior angles on the same side of the transversal
B. making a linear pair
C. complementary
D. supplementary

To determine the relationship between the given angles \(x - 10^\circ\) and \(190^\circ - x\), we analyze their sum:

1. **Sum of the two angles**:
\[
(x - 10^\circ) + (190^\circ - x) = x - 10^\circ + 190^\circ - x
\]
Simplify:
\[
= 180^\circ
\]

2. **Interpretation**:
When the sum of two angles is \(180^\circ\), the angles are **supplementary**.

3. **Options Analysis**:
- **A. Interior angles on the same side of the transversal**: This is incorrect because the problem does not mention a transversal or parallel lines.
- **B. Making a linear pair**: This is incorrect because the angles are not explicitly stated to be adjacent or forming a straight line.
- **C. Complementary**: This is incorrect because complementary angles sum up to \(90^\circ\), not \(180^\circ\).
- **D. Supplementary**: This is correct since the angles add up to \(180^\circ\).

**Final Answer**: D. Supplementary