Question

如图,若BP,CP,分别是∠ABC与∠ACB的外角平分线,且相交于P,则∠A于∠BPC存在的数量关系是:∠BPC=___

Answer 1

∠PBC=1/2(180°-∠ABC)=>∠ABC=180°-2∠PBC

∠PCB=1/2(180°-∠ACB)=>∠ACB=180°-2∠PCB

∠A=180°-(∠ABC+∠ACB)

=180°-(180°-2∠PBC+180°-2∠PCB)

=2(∠PBC+∠PCB)-180°

=2(180°-∠BPC)-180°

=180°-2∠BPC

∠BPC=90°-∠A/2