The diagonals of the rectangle KMNP intersect at point O. Find the corners of the triangle KOM

The diagonals of the rectangle KMNP intersect at point O. Find the corners of the triangle KOM if the angle KNP = 80 degrees.

Problems of this type can be solved in different ways. The main thing is to remember that the diagonals in the rectangle form two pairs of equal isosceles triangles.
Consider an isosceles triangle ONP, in which we know by condition the angle at the base KNP = 80 °, respectively, and the second angle at the base NPO = 80 °. Let’s find the angle at the vertex of this triangle:
NOP angle = 180 ° – (KNP angle + NPO angle) = 180 ° – (80 ° + 80 °) = 180 ° – 160 ° = 20 °.
We examined triangle ONP, it is equal to triangle KOM. This means that the sides and angles of these triangles are equal.
Answer: The angles of the KOM triangle are 80 °, 80 °, 20 °.