6. In trapezoid $A B C D$ shown, $A D$ is parallel to $B C$, and $A B=6, B C=7, C D=$ $8, A D=17$. If sides $A B$ and $C D$ are extended to meet at $E$, find the resulting angle at $E$ (in degrees).
Solution: 90
Choose point $F$ on $A D$ so that $B C D F$ is a parallelogram. Then $B F=C D=8$, and $A F=A D-D F=A D-B C=10$, so $\triangle A B F$ is a 6-8-10 right triangle. The required angle is equal to $\angle A B F=90^{\circ}$.