Question

In the figure AP is the bisector of angle A , what is the ratio of the area of triangle APB and triangle APC​

Answer 1

∠A+∠B

Step-by-step explanation:

If 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