Find the main sides of an isosceles trapezoid, the base of which is 14 cm and 8 cm, and one of the corners is 120 degrees

Given:
isosceles trapezoid ABCE,
BC = 8 centimeters,
AE = 14 centimeters,
angle ABC = angle ALL = 120 degrees.
Find the lengths AB, CE -?
Decision:
1. Consider an isosceles trapezoid ABCE. Angle A = angle E = (360 – 120 – 120): 2 = 120: 2 = 60 (degrees).
2. Let’s draw the heights VN, SR.
3. Right-angled triangles BHA and CPE are equal in hypotenuse and acute angle. Angle ABN = angle RFE = (180 – 90 – 60) = 30 degrees. Then AB = 2 * AN.
4. BC = HP = 8 centimeters, AH = PE = (14 – 8): 2 = 8: 2 = 4 (centimeters).
5. AB = 2 * 4 = 8 (centimeters).
Answer: 8 centimeters.