Hilbert's Foundations: Proving the Congruent Supplements Theorem - Expii

Typically, supplementary angles are defined as any angles whose measures sum to 180 degrees. But since Hilbert's system doesn't use the real numbers or degree measures, he defines supplementary angles basically as two angles that form a straight line. A good explanation here would give Hilbert's definition of supplementary angles and prove the Congruent Supplements Theorem.