so.. let's say ∡AGB and ∡BGC are say "a" units wide, and ∡CGD and ∡DGE are "b" units wide
notice the picture below
all angles added up together, will make up just a flat line, or 180°
now, notice in the picture, the ∡BGD is really just " a + b " wide, notice the green angle in the picture of ∡BGD, well, we know what a + b is