 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says in figure 6.29 F, AB is parallel to CD, CD is parallel to EF and Y is to Z is equal to 3 is to 7 find X. So let us begin with the solution and first let us write what we are given. First we have AB is parallel to CD also line CD is parallel to EF and Y is to Z is equal to 3 is to 7 and we have to find the value of X. Now since the ratio of Y and Z is 3 is to 7 therefore let Y is equal to 3T and Z is equal to 7T. Where T is any real number. Now let us see this figure and name this angle as U. Now since CD is parallel to EF then angle U will be equal to angle Z since they are alternate interior angles and Z is 7T therefore U will also be equal to 7T. Let us write down T is parallel to EF let this transpose be PQ. U will be equal to Z since they are alternate interior angles U is equal to 7T therefore Y plus U is equal to 180 degree since they form a linear pair and Y is equal to 3T and U is equal to 7T is equal to 180 degree this implies that 10T is equal to 180 degree or T is equal to 18 degree implies that angle Y which is equal to 3T is equal to 3 into 18 substituting the value of 18 we have 54 degree. So angle Y is equal to 54 degree now we have to find X. Now line AB is parallel to CD this implies X plus Y is equal to 180 degree since sum of consecutive interior angles is 180 degree therefore we have AB parallel to CD PQ is a transversal this implies X plus Y is equal to 180 degree since sum of consecutive interior angles supplementary that is 180 degree. Now let us substitute the value of Y which is 54 degree we get X is equal to 180 degree minus 54 degree which is equal to 126 degree thus is equal to 126 degree. So this completes the solution hope you enjoyed it take care and bye for now.