In rhombus ABCD, the diagonals meet at point O. Angle BAD = 50 degrees. Find the angles of triangle BOC.
| April 3, 2021 | education
In a rhombus, the sum of opposite angles is 180, then the angle ABC = 180 – BAD = 180 – 50 = 130.
The opposite angles of the rhombus are equal to each other, then the angle ВСD = BAD = 50.
The diagonals of the rhombus divide the angles at the vertices of the rhombus in half, and a right angle is formed at the point of intersection of the diagonals. Then the triangle BOС is rectangular, the angle BCO = BCD / 2 = 50/2 = 25, the angle СВO = ABC / 2 = 130/2 = 65.
Answer: The angles of the BOC triangle are 25, 65, 90.
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