 Hi and welcome to the session, I am Asha and I am going to help you with the following question that says in figure 6.41 if A B is parallel to D angle B A C is equal to 35 degree and angle C D E is equal to 53 degree find angle D C E that is we have to find this angle. So let us begin with the solution and we are given that A B is parallel to D angle B A C is equal to 35 degree and angle C D E is equal to 53 degree and we have to find angle D C E. Now since A B is parallel to D A E be the transversal and this implies angle E D will be equal to angle B as this angle is equal to this angle since it is a pair of alternate interior angles. These are intersected by a transversal and the two lines are parallel then the alternate interior angles are equal. Now angle B A C is 35 degree so this implies angle A E D is also 35 degree or we can say angle C E D is 35 degree. Let us number this equation as equation number 1. Now in triangle D C E sum of three angles angle D C E plus angle C E D plus angle E D C is equal to 180 degree since in a triangle sum of three angles is equal to 180 degree. Now angle D C E we have to find out angle C E D is 35 degree this is from equation number 1 plus angle E D C is given to us which is 53 degree which is equal to 180 or we can say that angle D C E plus on adding 35 with 53 get 88 is equal to 180 degree or we can say that angle D C E is equal to 92 degree our answer is angle D C E is equal to 92 degree which completes solution hope you enjoyed it take care and bye for now