Find the angle \(\angle NFL\)

Geometry Level 3

Let \( \triangle ABC \) be an acute triangle with angles 30, 70 and 80 (degrees) at vertices \(A\), \(B\), \(C\) respectively. Altitudes \(AP, BQ\) and \(CR\) intersects in the orthocenter \(H\) of \( \triangle ABC\). Points \(N, L\) on sides \(BC\) and \(AC\) are such that segment \(NL\) contains \(H\) and \(NL\) bisects \( \angle AHQ\). The point \(F\) on the circumcircle of \( \triangle ABC\) bisects the smaller arc \( AB \). Find \(\angle NFL \) in degrees.

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