There are (15-2)*180 = 2340 degrees in the regular 15-gon
2340/15 = 156 degrees in each of the corner pockets.
Connecting the lines from the vertices to the center creates
15 triangles, and they are all congruent by SSS.
So that leaves 78 degree base angles for each triangle, which
makes the angle from the center opposite the base 180 - 78 - 78 = 24.