In what direction should a line be drawn through the point (1, 2) so that its point of intersection with the line x + y = 4 is at a distance $ \large\frac{\sqrt 6}{3}$ from the given point

Question

$\begin {array} {1 1} (A)\;15^{\circ} \: or\: 75^{\circ} & \quad (B)\;30^{\circ} \: or \: 60^{\circ} \\ (C)\;45^{\circ} & \quad (D)\;60^{\circ} \: or \: 120^{\circ} \end {array}$