The angle between the diagonals of an isosceles trapezoid opposite to the base is 80 degrees

| January 9, 2021 | education

The angle between the diagonals of an isosceles trapezoid opposite to the base is 80 degrees, and the side is equal to the larger base. Find the corners of the trapezoid.

By condition, the AВСD trapezoid is isosceles, therefore its diagonals are equal and at the point of their intersection are divided in half.
Then AO = DO, and the angle OAD = ODA = (180 – 80) / 2 = 50.
Consider a triangle AСD, in which, according to the condition, the segment BP = СD, then the triangle is isosceles, and the angle AСD = СBP = 500. Then the angle ADС = 180 – 50 – 50 = 80.
The sum of the angles at the lateral sides of the trapezoid is 180, then the ВСD angle = 180 – ADС = 180 – 80 = 100.
In an isosceles trapezoid, the angles at the bases are equal, then:
Angle ABC = ВСD = 100, angle ABC = СDA = 80.
Answer: The angles of the trapezoid are equal to A = D = 80, B = C = 100.



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