1.

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»

Answer:

ANSWER

∠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


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