We know that l∥m and t is transversalfrom the figure we know that ∠APR and ∠PRD are alternate angles∠APR=∠PRDWe can write it as1/2∠APR=1/2∠PRDWe know that PS and RQ are the bisectors of ∠APR and∠PRDso we get∠SPR=∠PRQhence, PR intersects PS and RQ at points P and R respectivelyWe getPS∥RQin the same way SR∥PQtherefore, PQRS is a parallelogramwe know that the interior angles are supplementary∠BPR+∠PRD=180ofrom the figure we know that PQ and RQ are the bisectors of ∠BPR and ∠PRDWe can write it as2∠QPR+2∠QRP=180oDividing the equation by 2∠QPR+∠QRP=90o.....(1)Consider △PQRUsing the sum property of triangle∠PQR+∠QPR+∠QRP=180oby substituting in equation (1)∠PQR+90o=180o∠PQR=90oWe know that PQRS is a parallelogramit can be written as∠PQR=∠PSR=90oWe know that the adjacent angles in a parallelogram are supplementary∠SPQ+90o=180o∠SPQ=90oWe know that all the interior angles of quadrilateral PQRS are right angles therefore it is proved that the quadrilateral PQRS are right anglestherefore it is proved that the quadrilateral formed by the bisectors of interior angles is a rectangle.