If bisectors of angle A and angle B of a quad | vedclass

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(D) In quadrilateral $ABCD$,the sum of interior angles is $\angle A + \angle B + \angle C + \angle D = 360^{\circ}$.In $	riangle APB$,$\angle P + \fr

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quadrilateral whose opposite angles are supplementary

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(D) In quadrilateral $ABCD$,the sum of interior angles is $\angle A + \angle B + \angle C + \angle D = 360^{\circ}$.In $	riangle APB$,$\angle P + \frac{1}{2}\angle A + \frac{1}{2}\angle B = 180^{\circ} \implies \angle P = 180^{\circ} - \frac{1}{2}(\angle A + \angle B)$.Similarly,in $	riangle CRD$,$\angle R = 180^{\circ} - \frac{1}{2}(\angle C + \angle D)$.Adding these,$\angle P + \angle R = 360^{\circ} - \frac{1}{2}(\angle A + \angle B + \angle C + \angle D) = 360^{\circ} - \frac{1}{2}(360^{\circ}) = 360^{\circ} - 180^{\circ} = 180^{\circ}$.Since the sum of opposite angles $\angle P + \angle R = 180^{\circ}$,the quadrilateral $PQRS$ is a cyclic quadrilateral,meaning its opposite angles are supplementary.

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

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