The diagonal of the rectangle makes an angle of 58 with its side. Find the angle between the diagonals of the rectangle.
| June 21, 2021 | education
The diagonals of the rectangle, at the points of their intersection, are divided in half, therefore, ОА = ОD = ОВ = ОВ.
Then the triangles AOD, AOB, COB, COD are isosceles and their angles at the base are equal.
The angle OAB = OBA = 58, then the angle AOB = 180 – 58 – 58 = 64.
The angle BOD is expanded and is equal to 180, then the angle AOD = BOD – AOB = 180 – 64 = 116.
Answer: The angles between the diagonals are 64 and 116.
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