Answer:
[tex]m\angle B=m\angle C=120^{\circ}[/tex]
[tex]m\angle A=m\angle D=60^{\circ}[/tex]
Step-by-step explanation:
Trapezoid ABCD is isosceles trapezoid, because AB = CD (given). In isosceles trapezoid, angles adjacent to the bases are congruent, then
- [tex]\angle A\cong \angle D;[/tex]
- [tex]\angle B\cong \angle C.[/tex]
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:
[tex]AB=2AK.[/tex]
If in the right triangle the hypotenuse is twice the leg, then the angle opposite to this leg is 30°, so,
[tex]m\angle ABK=30^{\circ}[/tex]
Since BK ⊥ AD, then BK ⊥ BC and
[tex]m\angle KBC=90^{\circ}[/tex]
Thus,
[tex]m\angle B=30^{\circ}+90^{\circ}=120^{\circ}\\ \\m\angle B=m\angle C=120^{\circ}[/tex]
Now,
[tex]m\angle A=m\angle D=180^{\circ}-120^{\circ}=60^{\circ}[/tex]
