Answer
The angle between the positive direction of the x axis and the electron’s direction of motion is $~~0^{\circ}$
Work Step by Step
By conservation of momentum, the electron must move in the photon's original direction of motion since the photon scatters at an angle of $180^{\circ}$
Note that the photon's original direction of motion was in the positive direction of the x axis.
Therefore, the angle between the positive direction of the x axis and the electron’s direction of motion is $~~0^{\circ}$
