Question

在三角形ABC中,∠ABC和∠ACB的外角平分线相交于点P,探索∠A和∠BPC之间的数量关系.

Answer 1

关系为：

∠BPC=90°-1/2∠A

∠BPC

=180°-(∠PBC+∠PCB)

=180°-(∠B外角+∠C外角)/2

=180°-(∠A+∠C+∠A+∠B)/2

=180°-(180°+∠A)/2

=180°-90°+∠A/2

=90°-1/2∠A