In a rectangular trapezoid, the angle is C 135 degrees, the side of the BC is 3 cm. AB is 2 cm larger than BC. Find AD.

If BC = 3 cm, then AB = 5 cm. Since the trapezoid is rectangular, angle A = angle B = 90 degrees. Find the ADC angle:

90 + 90 + 135 + x = 360;

x = 45.

Let us drop the perpendicular CS from the vertex C. As a result, a right-angled CSD triangle was obtained from a right angle S. In this triangle, the SDC angle is equal to the SCD angle of 45 degrees. Side CS = AB = 5 cm. Side SD = SC = 5 cm, since the triangle is also isosceles. Side BC = AS = 3 cm.

Find the AD side:

AD = AS + SD;

AD = 3 + 5 = 8 cm.

Answer: 8 cm.