The diagonals of the KMNP rhombus intersect at point 0. Find the angles of the KOM triangle

The diagonals of the KMNP rhombus intersect at point 0. Find the angles of the KOM triangle if the MNP angle is 80 degrees

The diagonals of the rhombus intersect at right angles, so ∠KOM = ∠MON = ∠NOP = ∠KOP. Triangles KMN and KPN are equal, that is, ∠MNO = ∠NOP = 80/2 = 40 degrees. The MCO angle is symmetrically opposite to the MNO angle and is also 40 degrees.

The sum of all the angles of the triangle is 180 degrees.

∠KMO = 180 – 90 – 40 = 50 degrees.

Answer: ∠KOM = 90, ∠KMO = 50, ∠MCO = 40.