The diagonals of an isosceles trapezoid are the bisectors of its angles, and the angle between the diagonals is 30 °
| March 8, 2021 | education
The diagonals of an isosceles trapezoid are the bisectors of its angles, and the angle between the diagonals is 30 °. Find the corners of the trapezoid.
The angle AOD is adjacent to the angle COD, the sum of which is 180, then the angle AOD = 180 – 30 = 150.
Since the trapezoid is isosceles, its diagonals, at the point O, are divided into equal segments. ОА = ОD, ОВ = ОС, and then the triangles BOС and AOD are isosceles, which means the angle ОАD = АDA = (180 – 150) / 2 = 15.
AC and BD are the bisectors of angles A and D, then the angle BAD = CDA = 2 * 15 = 30.
The sum of the angles at the side of the trapezoid is 180, then the angle ABC = BCD = (180 – 30) = 150.
Answer: The angles of the trapezoid are 30, 30, 150, 150.
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