Euclid's Elements, Book I: Proposition 18
In any triangle, the greater side subtends the greater angle.
In other words, the greatest side of a triangle will be directly opposite of the greatest angle of a triangle.
1) We have triangle ABC, where side AC is greater than side AB.
2) We then say that angle ABC is also greater than angle ACB.
3) Since side AC if greater than side AB, let segment AD be made to equal length of AB. (I. 3)
4) Let BD be joined to create a segment.
5) Since angle ADB is an exterior angle of the newly created triangle BCD, it is greater than the interior and opposite angle DCB. (I. 16)
6) We also have that angle ADB is equal to ABD, as side AB is equal to side AD.
7) Thus, angle ABD is also greater than angle ACB.
8) Thus, angle ABC is also greater than angle ACB.
Done.