How to prove the sum of angles of traingle are 180
Well, for this you ust first know that an exterior angle of atringel equals the sume of the two triangle's angles which aren't besides it, and this is usually done precisely using the fact that the sum of any triangle's angle's is 180 deg.
Another way, perhaps more basic, to prove that is to choose any side of the angle and then through the opposite vertex to draw a line parallel to this side. Then, using the well known equalities between angles wrt parallel lines we get what we want.
Tonio