 Hi and welcome to the session, I am Arsha and I am going to help you with the following question with sense. In figure 6.16, if x plus y is equal to w plus z, then prove that a of v is a line. So, this is figure 6.16 and let us now begin with the solution. We are given that x plus y is equal to w plus z and we are required to prove that a of v is a line. Sum of four angles or we can say sum of all angles round a point which is in case, in this case it is o and where the sum of four angles will be equal to 360 degrees then sum of all angles round a point is equal to 360 degree. So, we will have sum of these four angles x plus y plus w plus z is equal to 360 degree. Now, we are given that x plus y is equal to w plus z. Therefore, on replacing x plus y by w plus z or replacing w plus z by x plus y, we will get two times of x plus y which is equal to 360 degree. Hence, x plus y is equal to w plus z which further implies that x plus y is equal to 180 degree or we can say that x is angle B O C and y is angle A O C is equal to 180 degree. Now, this implies angle B O C and angle A O C form a linear pair consequently O A and O B are opposite ways and therefore, A O B is a straight line. Hence, we know that sum of four in this case or we can say that sum of all angles at a point is equal to 360 degree. So, with the help of this idea, we have proved the above question. So, this completes the solution. Hope you enjoyed it. Take care and bye for now.