$\because AB=AC$，$\angle BAC=100^{\circ}$，
$\therefore \angle ABC=\angle ACB=\dfrac{1}{2}(180^{\circ}-\angle BAC0=50^{\circ}$，
$\therefore \angle ABM=40^{\circ}$，
$\because $四边形$BDEC$是矩形，
$\therefore \angle DBC=90^{\circ}$，
$\therefore \angle FBD=180^{\circ}-90^{\circ}-40^{\circ}=50^{\circ}$，
故选$C$.
