 Hi and welcome to the session. I am Arsha and I am going to help you with the following question which says in figure 6.28 find the values of x and y and then show that AB is parallel to CD. So let us begin with the solution and let us first write what we are given. Now on observing this figure you find that we are given two lines AB and CD such that a transversal let us name this transversal as PQ so a transversal PQ intersects then. Let us name the point of intersections as U and V. So the transversal PQ intersects them at U and V respectively and we have to find the values of x and y and also we have to show that AB is parallel to CD. From the figure we see that PQ is a line therefore sum of angle PUA and x is equal to 180 degree since they form a linear pair. So we have angle PUA plus x is equal to 180 degree. Now angle PUA is 50 degree so we have 50 degree plus x is equal to 180 degree. This implies that x is equal to 180 degree minus 50 degree which is equal to 130 degree. So x is equal to 130 degree. Now we have to find y. Now as we can see from the figure lines CD and PQ intersect at a point V intersect at a point V. Therefore angle CVQ is equal to y since they are vertically opposite angles. CVQ is 130 degree so 130 degree is equal to y thus we have y is equal to 130 degree. Hence we have x is equal to y but they are the alternate interior angles by transversal PQ with lines AB and CD and are equal. Therefore line AB is parallel to CD and this is the transverse of alternate angles its own. And thus our answers are x is equal to 130 degree, y is equal to 130 degree and we have shown that AB is parallel to CD. So this completes the solution. Hope you enjoyed it. Take care and bye for now.