Angle Chasing vex at times

Let $ABC$ be a triangle in which $\angle BAC = 80^{\circ}$ . Denote by $M$ the midpoint of segment $BC$ and consider a point $D$ on the open segment $AM$ such that $\angle BDC = 100^{\circ}$ . Consider point $F$ on the side $BC$ such that $DF$ bisects the angle $\angle BDC.$ Find the measure of $\angle BAF$ in degrees.