How Do You Relate These Points Now?

Geometry Level 5

Let \(O\) and \(H\) denote the circumcenter and the orthocenter of \(ABC\) respectively with midpoint of \(BC\) at \(M\).

The tangents at \(B,C\) to \(\odot ABC\) meet at \(D\). Construct \(AH\cap BC,\odot ABC=E,F\) respectively. \(FM\cap \odot ABC\) again at \(G\); \(N\) is the midpoint of \(AG\).

Suppose \(\angle A=50^{\circ}, \angle B=75^{\circ}\). Find \(\angle EDN+\angle HMB\) in degrees.

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