For a certain ray striking a plane mirror, the angle of incidence i is given by (3x+10)∘, while the angle between the incident and reflected rays is specified as (8x−20)∘.
(i) Establish an algebraic equation in x that relates the given angles.
(ii) Solve for x.
(iii) Using the value of x, determine the numerical values of the angle of incidence and the angle of reflection.
(iv) Verify quantitatively that the law of reflection is satisfied for this ray.