 Hello and welcome to the session. In this session we discussed the following question that says proof that the sum of the exterior angles of a quadrilateral is 360 degrees. Before moving on to the solution, let's recall that the sum of the angles of a quadrilateral is 360 degrees. This is the key idea for this question. Let's move on to the solution. Consider this quadrilateral ABCD where we have marked the interior angles of the quadrilateral as angle 2, 4, 5, 7 and the exterior angles 1, 3, 6, 8. Here, the interior and the exterior angles form a supplementary pair. Therefore, we get angle 1 plus angle 2 is equal to 180 degrees. We mark this as 1, then angle 3 plus angle 4 equal to 180 degrees. Let's mark it as 2, then angle 5 plus angle 6 as 180 degrees. Mark it 3, then we have angle 7 plus angle 8 equal to 180 degrees. Let's mark it equation 4. Now, since the sum of the angles of a quadrilateral is 360 degrees, therefore we have angle 2 plus angle 4 plus angle 5 plus angle 7 equal to 360 degrees. Let's mark it equation 5. Now, we add equations 1, 2, 3 and 4 and we get angle 1 plus angle 2 plus angle 3 plus angle 4 plus angle 5 plus angle 6 plus angle 7 plus angle 8 equal to 720 degrees. This can also be written as angle 1 plus angle 3 plus angle 6 plus angle 8 plus angle 2 plus angle 4 plus angle 5 plus angle 7 equal to 720 degrees. Now, using equation 5, we get angle 1 plus angle 3 plus angle 6 plus angle 8 plus 360 degrees is equal to 720 degrees. Since in equation 5, we have angle 2 plus angle 4 plus angle 5 plus angle 7 equal to 360 degrees. This gives us angle 1 plus angle 3 plus angle 6 plus angle 8 equal to 720 degrees minus 360 degrees which is equal to 360 degrees. Now, from this figure, as you can see that the exterior angles are angle 1, angle 3, angle 6 and angle 8. So, from this equation, we conclude that sum of the exterior angles of a quadrilateral is 360 degrees. Hence, proved. This completes the session. Hope you have understood the solution for this question.