check the picture below.
bearing in mind that a circle has a total of 360°, and a radius line coming from the center of the hexagon, will make an angle of 360°/6 or 60° for each side with the center of the circle, as you see in the picture.
if we run a bisector line through one of those 6 angles, we end up splitting it in two equal halves, namely two 30°, so that the apothem and the radius both coming from the center, with the side, make a 30-60-90 triangle, as you see there.
