Triangles and parallel lines problem

[lingping7]

The picture has the problem and my attempts, I need guidance.
Thanks in advance

 

[HallsofIvy]

Okay, you are given that angle 1 is congruent to angle 4 and angle 2 is congruent to angle 3 (you should say that in the proof). Angle 1 is congruent to angle 2 by "VOA" (vertical angles) so all of angles 1, 2, 3, and 4 are congruent to one another. To prove that AC is parallel to BD, you need to show that angle 4 is congruent to angle 6 or that angle 5 is congruent to angle 3 (alternate interior angles).

 

[lingping7]

Yes that is true, I'm able to get angle 5 = to angle 6, but can't equate either of these angles to angle 1,2,3,4

 

[ArcanaNoir]

How can you express the measure of angle 3? Can you express the measure of angle 5 in the same way?
[edit] I think I was transposing the 4 and the 6. >_<

 

[lingping7]

Angle 3 = 180-angle6-angle2
Angle 5 = 180-angle4-angle1
I could say Angle 5 = 180-angle2-angle2
I still don't get it :(