A regular polygon of m sides is exactly enclosed (no overlaps, no gaps) by m regular polygons of n sides each. (Shown here for m=4,n=8.) If m=10, what is the value of n?
[asy]
size(200);
defaultpen(linewidth(0.8));
draw(unitsquare);
path p=(0,1)--(1,1)--(1+sqrt(2)/2,1+sqrt(2)/2)--(1+sqrt(2)/2,2+sqrt(2)/2)--(1,2+sqrt(2))--(0,2+sqrt(2))--(-sqrt(2)/2,2+sqrt(2)/2)--(-sqrt(2)/2,1+sqrt(2)/2)--cycle;
draw(p);
draw(shift((1+sqrt(2)/2,-sqrt(2)/2-1))*p);
draw(shift((0,-2-sqrt(2)))*p);
draw(shift((-1-sqrt(2)/2,-sqrt(2)/2-1))*p);[/asy]
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>14<spanclass=′latex−bold′>(D)</span>20<spanclass=′latex−bold′>(E)</span>26