 Hello and welcome to the session. In this session we discussed the following question which says in the given figure find the values of x and y. First let's recall some facts which says that the sum of the angles of a triangle is 180 degrees and also if the side of a triangle is produced then the exterior angle so formed is equal to the sum of the two interior opposite angles. This is the key idea for this question. Now we shall move on to the solution. This is the figure given to us. Now let's see what all do we have in this figure. We are given that angle PQR is equal to y degree, angle QRP is equal to x degrees, angle RPQ is equal to 30 degrees and angle PRS is equal to 60 degrees and we need to find the values for x and y. Now as you can see the side QR of triangle PQR is produced. Therefore the exterior angle so formed that is angle PRS is equal to the sum of the interior opposite angles that is angle RQP plus angle QPR. Now substituting the values for the angles we get 60 degrees that is angle PRS is equal to angle RQP which is y degrees plus angle QPR which is 30 degrees. So this means we get y degrees is equal to 60 degrees minus 30 degrees. So we have y degrees is equal to 30 degrees or we can say that y is equal to 30. So we have got the value for y. Now we should find the value for x. For this we consider the triangle PQR in this angle RQP plus angle QPR plus angle QRP is equal to 180 degrees since we know that the sum of the angles of a triangle is 180 degrees. So substituting the values for these angles we get angle RQP which is y degrees or you can say 30 degrees plus QPR which is 30 degrees plus QRP which is x degrees is equal to 180 degrees. So this further gives us 60 degrees plus x degrees is equal to 180 degrees that is x degrees is equal to 180 degrees minus 60 degrees. So we get x degrees is equal to 120 degrees or you can say that x is equal to 120. So our final answer is x equal to 120 and y equal to 30. So this completes the session. Hope you have understood the solutions for this question.