The bisector of the angle between the diagonal and the height of the rhombus drawn from one vertex
| August 10, 2021 | education
The bisector of the angle between the diagonal and the height of the rhombus drawn from one vertex forms an angle of 20 degrees with this height. Find the corners of the diamond.
The height BH of the rhombus ABCD forms a right-angled triangle BDH, in which one of the acute angles is 20.
Then the angle ВDН = (180 – 90 – 20) = 70.
The diagonals of the rhombus are also the bisectors of the angles at the vertices of the rhombus, then the angle ADC = 2 * BDA = 70 * 2 = 140.
The sum of the adjacent angles of the rhombus is 180, then the angle BAD = (180 – 140) = 40.
The opposite angles of the rhombus are equal, then the angle BCD = BAD = 40, the angle ABC = ADC = 140.
Answer: The angles of the rhombus are 40, 140.
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