Find the angles of an isosceles trapezoid if one of its angles is 26 ° less than the other.

Let ABCD be an isosceles trapezoid, AB and CD the sides, AD and BC the bases. In an isosceles trapezoid, the angles at the base are equal, then: angle A = angle D, angle B = angle C.
Let angle A = angle D = x – 26, then angle B = angle C = x.
By the theorem on the sum of the angles of a quadrangle:
angle A + angle B + angle C + angle D = 360 degrees;
x – 26 + x + x + x – 26 = 360;
4x = 360 +52;
4x = 412;
x = 412/4;
x = 103.
Angle A = angle D = 103 – 26 = 77 (degrees), angle B = angle C = x = 103 degrees.
Answer: angle A = 77 degrees, angle B = 103 degrees, angle C = 103 degrees, angle D = 77 degrees.