In an isosceles trapezoid ABCD angle B = 135 BC = 10cm. AD = 18cm. Find the height BE.

In the resulting triangle ABE, the angle of trapezoid B is divided into two angles. One is 90 degrees and the other is 135-90 = 45 degrees and this angle is the angle of the ABE triangle. The height is the perpendicular to the opposite side, so the angle E of the triangle is 90 degrees.
The third angle of the triangle is 180- (45 + 90) = 45 degrees, that is, the triangle is isosceles.
Let’s drop the perpendicular from the corner C. The formed two triangles are equal.
Find side AE ​​of triangle ABE. (18-10) / 2 = 4 cm. Side AE ​​= BE as sides lying opposite equal angles.
Answer: Height BE = 4 cm.