Comparing angles in Euclid's Elements

Abstract: The exposition in Euclid's Elements contains an obvious gap (seemingly unnoticed by most commentators): he often compares not just angles, but groups of angles, and at the same time he avoids summing angles (and considering angles greater than $\pi$), and does not say what such a comparison of groups could mean. We discuss the problem and suggest a possible interpretation that could make Euclid's exposition consistent.