MP = MP, so triangle MPN ≅ triangle MPK by SSS. That means ∠NMP ≅ ∠KMP by CPCTC, so
... ∠NMP + ∠PMK = ∠NMK
... 2×∠PMK = 50° . . . substitute ∠PMK for ∠NMP, with which it is congruent
... ∠PMK = 25° . . . . . divide by 2
