8. 如图，$△ ABC$的外角$∠ ACD$的平分线与线段$BA$延长线交于点$F$，点$E$在线段$CF$上，且$∠ AEF+∠ FCD=180°$.
(1) 求证：$AE// BC$；
(2) 若$∠ B=28°$，$∠ ACF=62°$，求$∠ BAC$的大小.

8. (1) $\because ∠ AEF+∠ AEC=180°$，$∠ AEF+∠ FCD=180°$，$\therefore ∠ AEC=∠ FCD$，$\therefore AE// BC$ (2) $\because CF$是$∠ ACD$的平分线，$∠ ACF=62°$，$∠ B=28°$，$\therefore ∠ ACD=2∠ ACF=124°$，$\therefore ∠ BAC=∠ ACD-∠ B=124°-28°=96°$

9. (1) 已知：$AD$，$BC$相交于点$O$，连接$AB$，$CD$.证明：$∠ A+∠ B=∠ C+∠ D$.
(2) 如图②，$AP$，$CP$分别平分$∠ BAD$，$∠ BCD$，若$∠ ABC=36°$，$∠ ADC=16°$，求$∠ P$的度数.
(3) 如图③，直线$AP$平分$∠ BAD$，$CP$平分$∠ BCD$的外角$∠ BCE$.猜想$∠ P$与$∠ B$，$∠ D$的数量关系并证明.

9. (1) $\because ∠ A+∠ B+∠ AOB=180°$，$∠ C+∠ D+∠ COD=180°$，$\therefore ∠ A A+∠ B+∠ AOB=∠ C+∠ D+∠ COD$，$\because ∠ AOB=∠ COD$，$\therefore ∠ A+∠ B=∠ C+∠ D$ (2) $\because AP$，$CP$分别平分$∠ BAD$，$∠ BCD$，$\therefore ∠ BAP=∠ PAD$，$∠ BCP=∠ PCD$，由(1)的结论，得$∠ P+∠ BCP=∠ ABC+∠ BAP$ ①，$∠ P+∠ PAD=∠ ADC+∠ PCD$ ②，①+②，得$2∠ P+∠ BCP+∠ PAD=∠ BAP+∠ PCD+∠ ABC+∠ ADC$，$\therefore 2∠ P=∠ ABC+∠ ADC$，$\because ∠ ABC=36°$，$∠ ADC=16°$，$\therefore 2∠ P=36°+16°=52°$，$\therefore ∠ P=26°$ (3) $∠ P=90°+\frac{1}{2}(∠ B+∠ D)$，理由如下：$\because$ 直线$AP$平分$∠ BAD$，$CP$平分$∠ BCD$的外角$∠ BCE$，$\therefore ∠ PAB=∠ PAD$，$∠ PCB=∠ PCE$.$\therefore 2∠ PAB+∠ B=180°-2∠ PCB+∠ D$，$\therefore 180°-2(∠ PAB+∠ PCB)+∠ D=∠ B$，$\because ∠ P+∠ PAD=∠ PCB+∠ AOC=∠ PCB+∠ B+2∠ PAD$，$\therefore ∠ P=∠ PAD+∠ B+∠ PCB=∠ PAB+∠ B+∠ PCB$，$\therefore ∠ PAB+∠ PCB=∠ P-∠ B$.$\therefore 180°-2(∠ P-∠ B)+∠ D=∠ B$，即$∠ P=90°+\frac{1}{2}(∠ B+∠ D)$