The angle of incidence is the angle between the incident ray and the normal or in other words the angle between the oncoming ray of light and the normal vector of the surface of the material it is coming into contact with, while the angle of refraction is the angle between the refracted ray and the normal when light travels from one medium to another.
We can work out the angle of refraction and that of incidence without measuring by using Snell's Law.
Snell's Law states the relationship between the angle of incidence and the angle of refraction, such that the ratio of sine of angle of incidence to the sine of angle of refraction is always a constant.
That is; Sin i/Sin r, This is equivalent to the refractive index between the two medium used.