The diagonals of the KMNP rhombus meet at point O. Find the angles of the KOM triangle if the KNP angle is 80 degrees.

By the property of the diagonals of the rhombus, the diagonals are the bisectors of the angles at the vertices of the rhombus, then the angle KNM = KNP = 80. In the rhombus, the opposite angles are equal, then the angle PNM = PKM, which means the angle MKO = 80.

The diagonals of the rhombus intersect at point O at a right angle, which means the angle KOM = 90.

Then the angle KMO = 180 – 90 – 80 = 10.

Answer: The angles of the triangle KOM are equal to 90, 80, 10.