Question

In the figure abcd is a quadrilateral in which ap and bp are the bisectors of angle a and angle b respectively. dq and cq are the bisectors of angle d and c respectively. 1. find the value of angle rqs is rps = 70.

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