A ray from a fixed object is incident on a plane mirror at an angle of 20°. If the mirror is rotated through 30° by how many degrees would the reflected ray change its direction?

The mirror is rotated through an angle of $30^\circ$. Let this be $\theta$.

When a plane mirror is rotated by an angle $\theta$ about an axis in its plane, and the incident ray is kept fixed, the reflected ray rotates by an angle $2\theta$ in the same direction.

The angle of rotation of the reflected ray is $2\theta$.

The reflected ray would rotate by $60^\circ$.

The final answer is $\text{60 degrees}$.