Which of the following letters has a rotational symmetry but no line symmetry?

To determine which letter has rotational symmetry but no line symmetry, let's analyze each option step-by-step:

1. Understanding the Symmetries:
- Line Symmetry (Reflectional Symmetry): A figure has line symmetry if it can be divided by a line into two halves that are mirror images of each other.
- Rotational Symmetry: A figure has rotational symmetry if it looks the same after a rotation of more than $0°$ and less than $360°$ about its center.

2. Analyzing Each Option:
- M: Has a vertical line of symmetry down the center. It does not look the same when rotated by any angle other than $360°$. Thus, it has line symmetry but no rotational symmetry.
- O: Has multiple lines of symmetry (both vertical and horizontal) and also has rotational symmetry.
- Z: Has no line of symmetry (reflecting it vertically or horizontally does not yield the same letter). However, if you rotate the letter Z by $180°$ about its center, it looks exactly the same. Thus, it has rotational symmetry but no line symmetry.
- X: Has both vertical and horizontal lines of symmetry, and also has rotational symmetry (by $180°$).

Therefore, the letter that satisfies the condition of having rotational symmetry but no line symmetry is Z.