Is Angle Chasing Useful?

Geometry Level 4

In triangle \(ABC\), \(\angle{B} = 70^{\circ}\) and \(\angle{C} = 50^{\circ}\). Point \(M\) is placed on side \(AB\) such that \(\angle{MCB} = 40^{\circ}\) and point \(N\) is placed on side \(AC\) such that \(\angle{NBC} = 50^{\circ}\).

Find \(\angle{NMC}\) (in degrees).

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