Answer:
![m\angle B=m\angle C=120^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20B%3Dm%5Cangle%20C%3D120%5E%7B%5Ccirc%7D)
![m\angle A=m\angle D=60^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20A%3Dm%5Cangle%20D%3D60%5E%7B%5Ccirc%7D)
Step-by-step explanation:
Trapezoid ABCD is isosceles trapezoid, because AB = CD (given). In isosceles trapezoid, angles adjacent to the bases are congruent, then
Since BK ⊥ AD, the triangle ABK is right triangle. In this triangle, AB = 8, AK = 4. Note that the hypotenuse AB is twice the leg AK:
If in the right triangle the hypotenuse is twice the leg, then the angle opposite to this leg is 30°, so,
![m\angle ABK=30^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20ABK%3D30%5E%7B%5Ccirc%7D)
Since BK ⊥ AD, then BK ⊥ BC and
![m\angle KBC=90^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20KBC%3D90%5E%7B%5Ccirc%7D)
Thus,
![m\angle B=30^{\circ}+90^{\circ}=120^{\circ}\\ \\m\angle B=m\angle C=120^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20B%3D30%5E%7B%5Ccirc%7D%2B90%5E%7B%5Ccirc%7D%3D120%5E%7B%5Ccirc%7D%5C%5C%20%5C%5Cm%5Cangle%20B%3Dm%5Cangle%20C%3D120%5E%7B%5Ccirc%7D)
Now,
![m\angle A=m\angle D=180^{\circ}-120^{\circ}=60^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20A%3Dm%5Cangle%20D%3D180%5E%7B%5Ccirc%7D-120%5E%7B%5Ccirc%7D%3D60%5E%7B%5Ccirc%7D)