In rectangle ABCD, diagonals AC and BD meet at point O. Angle ABO = 40 °.
| September 3, 2021 | education
In rectangle ABCD, diagonals AC and BD meet at point O. Angle ABO = 40 °. Find Angles Between Diagonals of a Rectangle (Angle AOB and Angle BOC)
In a rectangle, the diagonals are equal, the intersection point divides them into equal parts.
Then the side AO = BO.
Therefore, triangle AOB is isosceles, angle ABO = BAO = 40 °.
So the angle AOB = 180º – 2 * 40º = 180º – 80º = 100º.
The BOC angle is adjacent to the AOB angle.
Therefore, BОС = 180º – 100º = 80º.
Answer: angle AOB = 100º, angle BOC = 80º
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