Proving Angle DBA + Angle DBC = 180: A Challenge!

[Pearce_09]

The question is:
Prove suppose A,B and C lie on a line L, with B between A and C, and that D is not on the line L. Prove that angle DBA + angle DBC = 180
this question is obvious. But because its obvious its hard to prove.
Say that X = angle DBA and Y = angle DBC
therefor cos(X + Y) = -1 ... I've gotten this far, i just don't know how to obtain anymore information
could i do cos(X) = u v/||u||||v|| and cos(Y) = v w/||v||||w||
where v is the vector shared with the two angles..
what do i do
thanks

 

[CarlB]

I don't think this is going to help, but

cos(X+Y) = cos(X)cos(Y)-sin(X)sin(Y)

and you could get the sine from the cross products.

Carl