The heights drawn from the top of the rhombus form an angle of 30 degrees. Find: a) the corners of the rhombus.

| September 25, 2021 | education

The heights drawn from the top of the rhombus form an angle of 30 degrees. Find: a) the corners of the rhombus. b) the angles that form the diagonals of the rhombus with its sides.

In the HBKD quadrangle, the angles BHD and BKD are equal to 90, since BH and BK are the heights of the rhombus, then the angle HDH = ADK = 360 – 90 – 90 – 30 = 150.

In a rhombus, the sum of adjacent angles is 180, and the opposite angles, at its vertices, are equal.

Then the angle BAD = BCD = 180 – 150 = 30, angle ABC = ADC = 150.

The diagonals of the rhombus are the bisectors of the angles at its vertices, then the angle BAO = BAD / 2 = 30/2 = 15, the angle ABO = ABC / 2 = 150/2 = 75.

Answer: The angles of the rhombus are 30 and 150, the angles between the diagonals and the sides of the rhombus are 15 and 75.



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