A. This is false because it should be angle 4 + angle 5 = 180 without the angle 6. Adding on angle 6 results in some angle larger than 180. Note how angle 5 = (angle 3)+(angle 6).
B. This is true and useful to showing that the three angles of a triangle add to 180 degrees. This is because you'll use the fact that angles 4, 5 and 6 combine to 180 degrees.
C. While this is a true statement by the exterior angle theorem, it is not useful to the proof. It is better to state that angle 2 and angle 6 are congruent because they are alternate interior angles.
D. Like choice C, it is true but not useful. It's better to say that angle 1 is congruent to angle 4. See choice B above.
Note how it's not enough for a statement to be true. It also needs to be relevant or useful to the context at hand. A more simpler example of this could be stating that x+x = 2x.
