AHSME 1995 Problem 17

Given regular pentagon $ABCDE$, a circle can be drawn that is tangent to $\overline{DC}$ at $D$ and to $\overline{AB}$ at $A$. The number of degrees in minor arc $AD$ is

$\mathrm{(A) \ 72 } \mathrm{(B) \ 108 } \mathrm{(C) \ 120 } \mathrm{(D) \ 135 } \mathrm{(E) \ 144 }$