If the mirror is turned through 15 degrees, then the angle of incidence becomes either 15 degrees more or, 15 degrees less.
Hence, the angle of reflection also changes by 15 deg more or by 15 deg less.
Thus, the angle between the incident ray and the reflected ray becomes 30 deg. more or 30 deg less. as compared to the original situation.
So answer is twice the angle of turn of the mirror.