The angle between the diagonals of the rectangle ABCD is 72 degrees. What is the angle
| July 13, 2021 | education
The angle between the diagonals of the rectangle ABCD is 72 degrees. What is the angle of the diagonal with the smaller side (AB)?
Since the diagonals in the rectangle, at the intersection point, are divided in half, the triangle and AOB are isosceles, OA = OB, and therefore the angles at the base of AB are equal, OBA = OAB.
Then 180 = 72 + ОАВ + ОВА = 72 + 2 * ОАВ.
OAB = (180 – 72) / 2 = 54.
Answer: The angle between the diagonal and the smaller side AB is 54.
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