Question

In the given figure, BP and CP are the bisectors of ZABC and ZACB respectively. Prove that
ZBPC = 90° + КР.
B

Answer 1

f AP and BP are angle bisector, then

∠1=∠2=∠A/2

∠3=∠4=∠B/2

And Consecutive angles are supplementary

∴∠1+∠2=180−(∠3+∠4)

∠A=180−∠B

From the figure, ∠APB=180−(∠1+∠3)

=180−(180−(∠2+∠4))

=∠2+∠4=∠A/2+∠B/2

⇒2∠APB=∠A+∠B

How satisfied are you with the answer?