Question

仅此而已∠A=40°,∠C=76°.BP为∠ABG的平分线,DP为∠CDG的平分线,求∠P的度数来张图！

Answer 1

如图所示,

∠A+∠ABC+∠AGB=∠C+∠CDG+∠CGD=180°

∠AGB=∠CGD

∴∠A+∠ABC=∠C+∠CDG

∴40°+∠ABC=76°+∠CDG

∴∠ABC=36°+∠CDG

∴1/2∠ABC=18°+1/2∠CDG

1/2∠ABC-1/2∠CDG=18°

∵∠DHB=∠A+1/2∠ABC=∠P+1/2∠CDG

∴∠P=∠A+1/2∠ABC-1/2∠CDG=40°+18°=58°

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