Question

In a triangle ABC, the internal bisectors of angle B and angle C meet at P and the external bisectors of angle B and angle C meet at Q, prove that angle BPC + angle BQC =180

Answer 1

Step-by-step explanation:

∠ABC+ext.∠∠ABC=180

o

(Angles on a straight line)

2

1

(∠ABC+ext.∠ABC)=90

o

∠PBC+∠QBC=90

o

(PB bisect Interior ∠B, QB bisects ext.∠B)

∠PBQ=90

o

Similarly, ∠PCQ=90

o

Sum of angles of quadrilateral PBCQ =360

o

∠BPC+∠PBQ+∠PCQ+∠BQC=360

o

∠BPC+∠BQC=180

o

∴∠BPQ+∠BQC = 2 rt. angles