9. [7] Let $A B C D$ be a trapezoid such that $A B \| C D, \angle B A C=25^{\circ}, \angle A B C=125^{\circ}$, and $A B+A D=C D$. Compute $\angle A D C$.
Answer:
$70^{\circ}$
Solution: Construct the parallelogram $A B E D$. From the condition $A B+A D=C D$, we get that $E C=A D=E B$. Thus,
$$
\angle A D C=\angle B E C=180^{\circ}-2 \angle B C E=180^{\circ}-2 \cdot 55^{\circ}=70^{\circ} \text {. }
$$