 Hi and welcome to the session and Asha and I am going to help you with the following question which says in figure 6.43 if PQ is perpendicular on PS, PQ is parallel to SR and angle SQR is equal to 28 degree and angle QRT is equal to 65 degree then find the values of X and Y. Let us now begin with the solution and here we are given PQ is perpendicular on PS this implies angle QPS is equal to 90 degree so this angle is 90 degree also we are given that PQ is parallel to SR let QR be the transversal which intersects them this implies angle PQR will be equal to angle QRT since if two lines are parallel and the transversal intersects them then the pair of alternate integer angles are equal so where alternate integer angles are equal now angle PQR is equal to X plus 28 degree and angle QRT is 65 degree so this implies X is equal to 65 degree minus 28 degree which is equal to 37 degree so we have X is equal to 37 degree so in the figure this angle is 37 degree now since sum of three angles of a triangle is 180 degree so in triangle PQS we have angle PQS plus angle QSP plus angle SPQ is equal to 180 degree and angle PQS is 37 degree which we have just found out angle QSP is Y and angle SPQ is 90 degree so this is equal to 180 degree which further implies Y is equal to 180 degree minus 90 degree minus 37 degree which is further equal to 53 degree thus Y is equal to 53 degree so this is 53 degree thus the values of X and Y are 37 degree and 53 degree so this completes the solution hope you enjoyed it take care and bye for now