smc

From consideration of a smaller regular polygon with an odd number of sides (e.g. a pentagon), we see that the lines of symmetry go through a vertex of the polygon and bisect the opposite side. Hence $L=15$, the number of sides / vertices. The smallest angle for a rotational symmetry transforms one side into an adjacent side, hence $R=360^{\circ }/15=24^{\circ }$, the number of degrees between adjacent sides. Therefore the answer is $L+R=15+24=\boxed{39}$.