The bisector NK is drawn in the MNP triangle, NK = KP, the angle NKP = 110 degrees. Find the angles M, MNP, P.

Consider the triangle NKP. In it, NK = KP (by condition). According to the definition of an isosceles triangle, we claim that the triangle NKP is isosceles. The angle NKP at the top is given by condition, we find the angles at the bottom:
KNP angle = KPN angle = (180 ° – NKP angle) / 2 = (180 ° – 110 °) / 2 = 35 °.
Find the corner MNP. Since NK is the bisector of the angle MNP (by condition), then the angle MNP = 2 * angle KNP = 2 * 35 ° = 70 °.
It remains to find the third corner in the triangle MNP.
NMP angle = 180 ° – (MNP angle + KPN angle) = 180 ° – (70 ° + 35 °) = 75 °.
Answer: in a triangle MNP the angles are equal: angle M 75 °, angle MNP 70 °, angle P 35 °.