One of the angles of an isosceles trapezoid is 74 degrees less than the other.

One of the angles of an isosceles trapezoid is 74 degrees less than the other. Calculate the degree measures of the remaining angles of the trapezoid. An explanation is required during the solution.

An isosceles trapezoid is a quadrangle, in which the sides are equal and the angles at the bases are equal.
Let ABCD be an isosceles trapezoid. Then angle A = angle D, angle B = angle C.
Let’s denote the angle B as x, then:
angle C = x (equal to angle B, since they are at the same base);
angle A = x – 74 (by condition, 74 degrees less);
angle D = x – 74 (equal to angle A, since they are at the same base).
By the theorem on the sum of the angles of a quadrangle:
angle A + angle B + angle C + angle D = 360 degrees;
x – 74 + x + x + x – 74 = 360;
4x -148 = 360;
4x = 360 + 148;
4x = 508;
x = 508/4 = 127 (degrees).
angle B = angle C = x = 127 degrees.
angle A = angle D = x – 74 = 127 – 74 = 53 (degrees).
Answer: angle A = 53 degrees, angle B = 127 degrees, angle C = 127 degrees, angle D = 53 degrees.