Question

AP and BP are the bisectors of ∠A and ∠B of quadrilateral ABCD. If ∠D = 100° <br /><br />and ∠C = 100°, find the measure of ∠APB.​

Answer 1

Answer:

ANSWER

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