The angle between an incident ray and a mirror is 60 degree. What is the total angle through which the ray of light turns?
The incident ray, the normal and the reflected ray are lie in one plane, the law of reflection says. Also, angles between normal and incident ray, and between normal and reflected ray are the same (normal is the straight line which is orthogonal to the mirror and goes through the point of incidence).
In a case of a plane mirror (I think this is the case) angles between mirror and both rays are also equal (as angles, complementary to equal ones).
Please look at the picture. Angle 1 is equal to 60 degrees -- this is given. Angle 2 is 60 degrees, too, by the law of reflection. And angle 3 also 60 degrees as a vertical angle to the angle 1.
Dashed line shows the continuation of the incident ray (as is there was no mirror). As picture shows, the angle between incident ray (its continuation) and reflected ray is (angle 2 + angle 3) = 120 degrees. This is the angle by which the ray of light turns.