Find the sides of an isosceles trapezoid whose bases are 40 cm and 32 cm if one of the angles is 120 °

Given:
ABCE is an isosceles trapezoid,
BC = 32 centimeters,
AE = 40 centimeters,
angle B = angle C = 120 degrees.
Find the length of the lateral sides AB = CE -?
Solution:
1) Consider an isosceles trapezoid angle A = angle E = (360 – 240): 2 = 120: 2 = 60 degrees.
2) Let’s draw the heights CO and BK. We get a rectangle BCOK. EO side = (40 – 32): 2 = 8: 2 = 4 (centimeters);
3) Consider a right-angled triangle COE. He has an OCE angle = 180 – 90 – 60 = 30 (degrees). Then OE = 1/2 * CE, CE = 2 * OE = 2 * 4 = 8 (centimeters).
Answer: 8 centimeters; 8 centimeters.