 Hello and welcome to the session. In this session, we discussed the following question which says two lines A, B and C, D intersect at a point O such that angle B O C plus angle A O D is equal to 260 degrees, find all the four angles. Before moving on to the solution, let's recall that the sum of the angles of a linear pair is 180 degrees and if two lines intersect then the vertically opposite angles are equal. This is the key idea for this question. Let's move on to the solution now. In this figure as you can see we have two lines A D and C D intersecting at a point O and in the question we are given that angle B O C plus angle A O D is equal to 260 degrees. Now as you can see that angle B O C and angle A O D are vertically opposite angles. So this means angle B O C is equal to angle A O D. We take let this be equal to x degrees. Now since we have angle B O C plus angle A O D is equal to 260 degrees. So we say x degrees plus x degrees is equal to 260 degrees that is 2x degrees is equal to 260 degrees and somewhere we get x degrees is equal to 130 degrees. That is angle B O C equal to angle A O D is equal to 130 degrees. Now from the figure you can see that angle A O C and angle B O C form a linear pair form since we know that the sum of the angles of a linear pair is 180 degrees. Thus we get angle A O C plus angle B O C is equal to 180 degrees. Now we have got the measure of angle B O C as 130 degrees. So we have angle A O C plus 130 degrees is equal to 180 degrees which gives us angle A O C equal to 180 degrees minus 130 degrees equal to 50 degrees. So we have got angle A O C equal to 50 degrees as you can see from the figure angle A O C and angle B O D are the vertically opposite angles and we know that vertically opposite angles are equal so angle A O C is equal to angle B O D. Now since angle A O C is equal to 50 degrees so we get angle B O D is also equal to 50 degrees. Thus we have got the measure of all the angles that is we have got angle A O C equal to 50 degrees, angle B O C is equal to 130 degrees, angle B O D is equal to 50 degrees and angle A O D is equal to 130 degrees. So with this we complete the session hope you have understood the solution for this question.