Question

如图,BP平分∠ABC交CD于F,DP交AB于E,DP平分∠ADC,AB与CD相交于O,若∠A=40°,∠C=36°,求

Answer 1

设∠ADP＝∠1,∠ABP＝∠2

∵BP平分∠ABC

∴∠ABC＝2∠2

∴∠AOC＝∠C+∠ABC＝∠C+2∠2

∵DP平分∠ADC

∴∠ADC＝2∠1

∴∠AOC＝∠A+∠ADC＝∠A+2∠1

∴∠A+2∠1＝∠C+2∠2

∴2（∠1-∠2）＝∠C-∠A

∵∠AEP＝∠A+∠1,∠AEP＝∠P+∠2

∴∠A+∠1＝∠P+∠2

∴∠1-∠2＝∠P-∠A

∴2（∠P-∠A）＝∠C-∠A

∴∠P＝（∠A+∠C）/2＝（40+36）/2＝38°