Oh nuh i think i only got the second angle wrong. The motor starts off parallel to the magnetic field, then moves 90 degrees where the torque reduces to zero. From THERE it completes 180 degrees, until the torque reaches zero. Yeah and this is right because the angle starts of at zero to the magnetic field (cos 0 = 1) at 90 degrees (cos 90 = 0) and it states that the communator changes the direction of the current when the torque reaches zero. Then from there it completes another 90 degree rotatation (180 degrees, cos 180 = -1, the torque is still not zero), then another 90 degrees until the current changes again (cos 270 = 0), the moves back to where it starts.
So to correct my post it should be:
The motor is able to completely rotate 360 degrees, by using a component called a "commutator" which consists of a split metal ring, which changes the direction of the current when the torque reaches 0. This is when the motor completes a 90 degree rotation (you said 180, but i think you meant 90). At this point, the direction of the current changes, and hence the forces change direction, completing another 180 degree rotation. This process is repeated again so that the motor is able to completely rotate 360 degrees.