Question

在△ABC中,∠A=40°,BO平分∠ABC,CO平分∠ACD.

Answer 1

∵∠ACD是△ABC的外角,∴∠ACD=∠A+∠ABC,∴∠A=∠ACD-∠ABC

∵∠OCD是△OBC的外角,∴∠OCD=∠O+∠OBC,∴∠O=∠OCD-∠OBC

又：BO平分∠ABC,CO平分∠ACD,∴∠OCD=1/2∠ACD,∠OBC=1/2∠ABC

∴∠O=∠OCD-∠OBC = 1/2∠ACD-1/2∠ABC = 1/2(∠ACD-∠ABC) = 1/2∠A = 1/2×40 = 20°