如图,在△ABC中,∠B的平分线与∠C的外角平分线相交于点D,则∠D=2分之1∠A

2025-05-19 02:49:59
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回答1:

∵∠DCE=∠D+∠DBE=∠D+1/2 ∠ABE
∵∠ACE=∠A+∠ABE
∵CD平分∠ACE, BC平分∠ABE,
∴∠DCE=∠D+1/2 ∠ABE=1/2(∠A+∠ABE)
∴∠D+1/2 ∠ABE=1/2∠A+1/2∠ABE
∴∠D=1/2∠A