角A=40度,角C=76度,BP为角ABG的平分线,DP为角CDG的平分线,求角P的度数

Question

角A=40度,角C=76度,BP为角ABG的平分线,DP为角CDG的平分线,求角P的度数

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°