The diagonals of the KMNP rhombus meet at point O. Find the angles of the triangle KOM if the angle MNP is 80 °.
| September 1, 2021 | education
In a rhombus, the opposite angles are equal, then the angle MKP = MNP = 80.
The sum of the adjacent angles of the rhombus is 180, then the angle KMN = 180 – 80 = 100.
The diagonals of the rhombus bisect the corners at the vertices and intersect at an angle of 90.
Then the angle MCO = MKP / 2 = 80/2 = 40.
Angle KMO = KMN / 2 = 100/2 = 50.
KOM angle = 90.
Answer: The angles of the KOM triangle are 40, 50, 90.
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