In rhombus ABCD, diagonals AC and BD meet at point O. Angle ADC = 108 degrees.
| August 11, 2021 | education
In rhombus ABCD, diagonals AC and BD meet at point O. Angle ADC = 108 degrees. Find the angles of triangle AOB (angle BAO, ABO, AOB)
In a rhombus, the diagonals intersect at right angles, which means that the AOB angle is 90 °.
The opposite angles of the rhombus are equal, which means that the angle ABC is also equal to 108 °.
In a triangle ABC, the sides AB = BC (the sides of the rhombus are equal), BO is not only the height, but also the bisector. This means that the angle ABO is equal to 1/2 of the angle ABC: 108 °: 2 = 54 °.
The sum of the angles in the triangle is 180 °, we find the angle of the BAO:
BAO = 180 ° – (ABO + AOB) = 180 ° – (54 ° + 90 °) = 180 ° – 144 ° = 36 °.
Answer: The angles of the AOB triangle are 90 °, 54 ° and 36 °.
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