如图1 角A=70°,BP.CP分别平分角ABC和角ACB,求角P

【第（1）题】根据三角形外角的性质,有∠ACD=∠A+∠ABC,∠PCD=∠P+∠PBC而,BP、CP分别是∠ABC、∠ACD的平分线,即有,∠PBC=(1/2)*∠ABC,∠PCD=(1/2)*∠A

∵∠ACD=∠A+∠ABC,CP平分∠ACD∴∠PCD=∠ACD/2=（∠A+∠ABC）/2∵BP平分∠ABC∴∠PBC=∠ABC/2∴∠PCD=∠P+∠PBC=∠P+∠ABC/2∴∠P+∠ABC/2

根据三角形外角的性质,有∠ACD=∠A+∠ABC,∠PCD=∠P+∠PBC而,BP、CP分别是∠ABC、∠ACD的平分线,即有,∠PBC=(1/2)*∠ABC,∠PCD=(1/2)*∠ACD代入化简得

∠BPC=115度

如下：∠ACD=∠ABC+∠A=∠ABC+70°∠PCD=1/2*∠ACD=1/2*∠ABC+35°∠PCD=∠PBC+∠P∠PBC+∠P=1/2*∠ABC+35°∠P=35°

∵AB=AC，∠A=40°，∴∠DBP=∠ECP=70°，又∵BP=CE，BD=CP，∴△DBP≌△PCE，∴∠BDP=∠EPC，又∵∠DBP=70°，∴∠DPB+∠BDP=110°，∴∠DPE=18

结论：∠P=1/2(∠A+∠D)[情况1]AB‖CD则∠PBC+∠PCB=1/2(∠ABC+∠BCD)=90°∠P=180°-90°=90°因为∠A+∠D=180°所以∠P=1/2(∠A+∠D)[情况

∠BPC+∠PBC+∠PCB=180∠BPC+1/2∠ABC+1/2∠ACB=180（1）∠A+∠ABC+∠ACB=1801/2∠A+1/2∠ABC+1/2∠ACB=90（2）（1）—(2)得:∠BP

角的负号不写了A+ABP=P+ACPA=P+ACP-ABPA=P+(1/2)(ACD-ABC)A=P+(1/2)A1/2A=PA=54度

∵∠ACD＝∠A+∠ABC,CP平分∠ACD∴∠PCD＝∠ACD/2＝（∠A+∠ABC）/2∵BP平分∠ABC∴∠PBC＝∠ABC/2∴∠PCD＝∠P+∠PBC＝∠P+∠ABC/2∴∠P+∠ABC/2

/>∵∠ACD＝∠A+∠ABC,CP平分∠ACD∴∠PCD＝∠ACD/2＝（∠A+∠ABC）/2∵BP平分∠ABC∴∠PBC＝∠ABC/2∴∠PCD＝∠P+∠PBC＝∠P+∠ABC/2∴∠P+∠ABC

∵∠ACD＝∠A+∠ABC,CP平分∠ACD∴∠PCD＝∠ACD/2＝（∠A+∠ABC）/2∵BP平分∠ABC∴∠PBC＝∠ABC/2∴∠PCD＝∠P+∠PBC＝∠P+∠ABC/2∴∠P+∠ABC/2

/>∵∠ACD＝∠A+∠ABC,CP平分∠ACD∴∠PCD＝∠ACD/2＝（∠A+∠ABC）/2∵BP平分∠ABC∴∠PBC＝∠ABC/2∴∠PCD＝∠P+∠PBC＝∠P+∠ABC/2∴∠P+∠ABC

这个算一下就好了啊.∠PBC=1/2(∠A+∠ACB)∠PCB=1/2(∠A+∠ABC)∠P=180°-上面两个也就是∠P=180°-∠A-1/2∠ACB-1/2∠ABC因为1/2∠ACB+1/2∠A

因为角A=64度所以角ABC+角ACB=180-64=116度所以角PBC+角PCB=(2*180-116)/2=122度所以角P=180-122=58度

∠A=50,所以∠ABC+∠ACB=130∠ACP=1/2（180-∠ACB）=90-∠ACB/2∠P=180-∠PBC-（∠ACB+∠ACP）因为∠PBC=∠ABC/2所以∠P=180-∠ABC/2

在BC延长线上取点E∵∠A+∠ABC+∠ACB＝180∴∠ABC+∠ACB＝180-∠A∵∠ACE＝180-∠ACB,CP平分∠ACE∴∠PCE＝∠ACE/2＝（180-∠ACB）/2＝90-∠ACB

∵∠BCP=12∠BCE=12（∠A+∠CBA），∠CBP=12∠CBD=12（∠A+∠ACB）；（角平分线的定义及三角形的一个外角等于与它不相邻的两个内角的和）∴∠BCP+∠CBP=∠A+12（∠C

∵∠A=86°,∴∠ABC+∠ACB=94°又∵BP平分∠ABC,CP平分∠ACB∴∠PBC=1/2∠ABC,∠PCB=1/2∠ACB.∴∠PBC+∠PCB=1/1(∠ABC+∠ACB）=47°.∴∠

∵∠A=60°∴∠ABC+ACB=120∵BP,BE和CP,CE三等分它们 ∴∠EBC∠+ECB=∠EBC+∠ECB=40 ∴∠BEC=140 ∴其外角为360-140=