I think it should be an ancient Greek mathematician who was interested in proving all triangle has inner angles summing to 180 degree? Was it Thales?
According to the Greek (Hellenistic) tradition, this was Thales. He is credited with proofs of such things as that "vertical angles formed by two lines are equal". But this was written in the Hellenistic histories of mathematics centuries after Thales, and we have no idea what sort of proofs he really gave to such things.
We really do not have primary sources for pre-Euclidean mathematics earlier than Euclid himself, and Euclid does not give credits.
One has to be very cautious about Hellenistic sources. For example they claim almost unanimously that Thales and Pythagoras studied mathematics in Egypt but according to modern historians mathematics in Egypt was on very primitive level, and it is not clear what they could possibly learn in Egypt. It seems that the Greeks invented the proofs themselves, at some time between Thales and Plato, but who and when exactly, we do not know.