In the triangle MNK, the angle K is 90 and the angle N is 50. On the ray KN, the segment

In the triangle MNK, the angle K is 90 and the angle N is 50. On the ray KN, the segment KP is plotted equal to KM. Find the angles of the triangle MNP.

Consider a triangle PKM – it is right-angled isosceles (KP = KM, by condition).
The angles at the base are equal, we get that the angle KPM = 90 ° / 2 = 45 °.
Let’s find the angle MNP, it is adjacent to the angle KNP = 50 ° (by condition).
Angle MNP = 180 ° – 50 ° = 130 °.
It remains to find the third unknown corner NMP.
Angle NMP = 180 ° – (130 ° + 45 °) = 180 ° -175 ° = 5 °.
Answer: The angles of the MNP triangle are 5 °, 45 °, 130 °.