In the MKE triangle it is known that MK = ME. Points F and N are marked on the KE side so that point N

In the MKE triangle it is known that MK = ME. Points F and N are marked on the KE side so that point N lies between points F and E, and the angle KMF = angle EMN. Prove that angle MFN = angle MNF.

1) Consider Δ MKF and Δ MEN
MK = ME (by condition) ⇒ ΔМКЕ – isosceles;
∠ К = ∠ Е (by the property of an isosceles triangle);
∠ KMF = ∠E MN (by condition);
Therefore, Δ MKF = Δ MEN;

2) ∠ MFN is the outer corner of the vertex F in ΔMKF
∠ MNF – outer corner of the vertex N in ΔMEN
∠ F = ∠ N (since Δ MKF = Δ MEN from n, 2) ⇒
∠ MFN = ∠ MNF (since the outer corners must be equal for equal vertices).