 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says in figure 6.32 if AB is parallel to CD angle APQ is equal to 50 degree and angle PRD is equal to 127 degree find X and Y. This is now begin with the solution and we are given that the line AB is parallel to CD angle APQ is equal to 50 degree and angle PRD is equal to 127 degree and we have to find the values of X and Y. Now since AB is parallel to CD, PQ any transversal this implies angle APQ is equal to angle PQR since if two parallel lines are intersected by a transversal then the pair of alternate interior angles are equal. These two angles are equal since they are alternate interior angles. Now angle APQ is equal to 50 degree and angle PQR is equal to X thus we have X is equal to 50 degree we have to find the value of Y. Now since AB is parallel to CD and let PR be the transversal which intersects them then this implies that angle APR is equal to angle PRD since they are alternate interior angles. Parallel lines are intersected by a transversal then the alternate interior angles are equal. Now angle APR is equal to Y plus 50 degree and PRD is 127 degree this implies Y is equal to 127 minus 50 which is equal to 77 degree thus Y is equal to 77 degree hence values of X and Y here 50 degree and 77 degree so this completes the solution hope you enjoyed it take care and bye for now.