Is Angle Chasing Useful?

Geometry Level 4

In triangle ABCABC, B=70\angle{B} = 70^{\circ} and C=50\angle{C} = 50^{\circ}. Point MM is placed on side ABAB such that MCB=40\angle{MCB} = 40^{\circ} and point NN is placed on side ACAC such that NBC=50\angle{NBC} = 50^{\circ}.

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

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