 Hi and welcome to the session, I am Asha and I am going to help you with the following question that says in figure 6.30 if A P is parallel to C D, E F is perpendicular on C D and angle G E D is equal to 126 degree, find angle A G E, angle G E F and angle F G E. So let us begin with the solution and we are given that A P is parallel to C D, E F is perpendicular on C D and angle G E D is equal to 126 degree and we have to find first angle A G E then we will find angle G E F and lastly we will find angle F G E. First let us find angle A G E. Now as A B is parallel to C D and G E be any transversal then angle A G E will be equal to angle G E D since they are alternating D D angles and angle G E D is equal to 126 degrees this implies angle A G E is also 126 degree. Let us now write down A B is parallel to C D and G is a transversal this implies that angle A G E is equal to angle G E D and G E D is equal to 126 degree so this implies that angle A G E is equal to 126 degree. Now let us find angle G E now we have to find angle G E F that is this angle. This angle we get when we subtract 90 degree from angle G E D and this angle is 90 degree since E F is perpendicular on C D so angle G E F is equal to angle G E D minus angle F E D and G E D is equal to 126 degree minus F E D is 90 degree since F E is perpendicular on C D this implies angle F E D is equal to 90 degree which further implies that angle G E F is equal to 36 degree and now let us find angle F G E F G E is this angle and this we get when we subtract 126 degree from 180 degree since this is a line and both these angles form linear pair. So we have to find angle F G E now A B is a line this implies angle A G E plus angle F G E is equal to 180 degree and angle A G E is 126 degree this is given to us plus angle F G E is equal to 180 degree which further implies angle F G E is equal to 180 degree minus 126 degree which is equal to 54 degree thus we have angle F G E is equal to 54 degree hence our answers are first we have to find angle A G E which is equal to 126 degree and we have to find angle G E F G E F which is 36 degree and lastly we have to find out angle F G E which is equal to 54 degree. So this completes the solution hope you enjoyed it take care and bye for now.