In a rectangular trapezoid, the angle difference at one of the lateral sides is 48 °. Find the corners of the trapezoid.

Given:
rectangular trapezoid ABCE,
angle E – angle C = 48 degrees,
Find the angles of a rectangular trapezoid ABCE, that is, angle A, angle B, angle C, angle E -?
Decision:
Consider a rectangular trapezoid ABCE. Angle A = Angle B = 90 degrees. Angle E = angle C + 48. We know that the sum of the degree measures of the parallelogram is 360 degrees.
Hence:
angle A + angle B + angle C + angle E = 360;
90 + 90 + angle С + angle С + 48 = 360;
180 + 2 * angle С + 48 = 360;
228 + 2 * angle C = 360;
2 * angle С = 360 – 228;
2 * angle C = 132;
angle C = 132: 2;
angle C = 66 degrees;
angle E = 66 + 48 = 114 degrees.
Answer: 90 degrees; 66 degrees; 114 degrees.