If bisectors of `angle A and angle B` of a quadrilateral ABCD intersect each other at P, of `angle B and angle C " at " Q, " of " angle C and angle D " at R and of " angle D and angle A ` at S then PQRS is a

Options

A. rectangle
B. parallelogram
C. rhombus
D. quardilateral whose opposite angles are supplementary

Answer

D

Explanation

`angle APB =180^(@)-((1)/(2)angle A + (1)/(2) angle B).`
`angle CRD =180^(@) -((1)/(2)angle C +(1)/(2) angle D).`
`therefore angle SPQ + angle SRQ =angle APB + angle CRD`
`=360^(@)-(1)/(2) (angle A +angle B+angle C+angle D)`
`=360^(@) -180^(@) =180^(@).`
Now, `angle PSR + angle PQR =360^(@)-(angle SPQ+angle SRQ)`
`=360^(@)-180^(@)=180^(@).`