The angle between the heights drawn through the apex of the obtuse angle of the rhombus is 30 °.

The angle between the heights drawn through the apex of the obtuse angle of the rhombus is 30 °. Find the corners of the rhombus.

Consider a quadrilateral КВМD, in which the angle КВМ, by condition, is equal to 30, and the angle ВКD = ВМD = 90, then the angle КDM = АDC = 360 – 90 – 90 – 30 = 150.

The sum of the adjacent angles of the rhombus is 180, then the angle BAD = 180 – 150 = 30.

In a rhombus, the opposite angles are equal, then the angle BCD = BAD = 30, the angle ABC = ADC = 150.

Answer: The angles of the rhombus are 30, 150, 30, 150.