In an isosceles trapezoid ABCD, angle A is 30 degrees greater than angle B. Find all the angles of the trapezoid.

By condition, the angle (ABC – BAC) = 30.

By the property of a trapezoid, the sum of its angles at the side of the trapezoid is 180.

Angle (ABC + ВAD) = 180.

Let’s solve two equations by the substitution method.

Angle ABC = 30 + ВAD.

Then: (30 + ВAD + ВAD) = 180.

2 * ВAD = 180 – 30 = 150.

Angle ВAD = 150/2 = 75.

Then the angle ABC = 75 + 30 = 105.

Since the trapezium is isosceles, the ВDA angle = ВAD = 75, the ВСD angle = ABC = 105.

Answer: The angles of the trapezoid are 75.105, 75, 105.