ABCD is a trapezoid, a diagonal AC is drawn, a right-angled triangle is obtained. AB = CD = BC. Find the corners of the trapezoid.

Since the triangle ABC, by condition, is isosceles, the diagonal AC is the bisector of the angle BCD.

Let the angle BAC = X0, then the angle ADC = X0, since the trapezoid is isosceles. Angle СAD = BAD / 2 = (X / 2) 0.

The ACD triangle is rectangular, then the sum of the angles (CAD + ACD + ADC) = 180.

(X / 2) + 90 + X = 180.

1.5 * X = 90.

X = 60.

Angle BAD = ADC = 60.

The sum of the angles at the side of the trapezoid is 180, then the angle ABC = BCD = 180 – 60 = 120.

Answer: The angles of the trapezoid are 60, 120, 60, 120.