A comparison of lengths

Let $AD,BE,CF$ be altitudes of an acute triangle $ABC$ with $AB > AC$ . Line $EF$ meets $BC$ at $P$ , and the line through $D$ parallel to $EF$ meets $AC , AB$ at $Q,R$ respectively. Let $N$ be a point on the side $BC$ such that $\angle NQP +\angle NRP = 178^\circ$ .

Which of the following is true?