Given Trapezoid ABCD AB = 8 cm, BC = 6 cm, AD = 14 cm, AB = CD find angle A and angle D

From the top of the obtuse angle C, we lower the height CH.

Since, by condition, AB = CD, the trapezoid is isosceles. The height CH, lowered from the apex of an obtuse angle, in an isosceles trapezoid divides the larger base into two segments, the smaller of which is equal to the half-difference of the lengths of the bases. DН = (АD – ВС) / 2 = (14 – 6) / 2 = 4 cm.

In a right-angled triangle CDH, the leg DH is two times less than the hypotenuse CD, which means that the angle is DCH = 30. Then the angle CDB = 180 – СНD – DCН = 180 – 90 – 30 = 60. In an isosceles trapezoid, the angles at the base are equal, then the angle BAD = CDA = 60.

Answer: Angle A and D are equal to 60.