ZA-SAMO 2014 Problem 3

In obtuse triangle $ABC$ , with the obtuse angle at $A$ , let $D$ , $E$ , $F$ be the feet of the altitudes through $A$ , $B$ , $C$ respectively. $DE$ is parallel to $CF$ , and $DF$ is parallel to the angle bisector of $\angle BAC$ . Find the angles of the triangle.