The statement about sum of the angles is a theorem in geometry. You doubtless remember from high-school geometry that you begin with certain axioms, or unproved statements, together with certain definitions of important terms to be used in the study, and from these you begin proving various theorems by showing that they can be deduced from certain of the axioms and definitions. Once you have proved the first theorem, you can get the second by means of it plus previous axioms and definitions. We do not use all of them all of the time: we may get Theorem 50 from Axioms 1 and 3 plus Theorems 3, 13, and 42, for example.