In the given figure, PA and SA are bisectors of two adjacent angles P and S of quadrilateral PQRS. Prove that 2 angle PAS= angle Q + angle R.

Given :
PORS is an quadrilateral and PA and SA is bisector of angle P and angle S respectively.

To prove : 
2 anglePAS = angle Q and angle R

Proof :
Let angle 1 be x and angle2 be y
x/2 + y/2 +2 angle PAS = 180
x+y+2 angle PAS = 360                                 ( multiplied 2 on both side)
x+y+2 angle PAS = x+y+ angle q+ angle R     (angle sum property of  quadrilteral)
2 angle PAS = angle Q + Angle R

hence proved.