 Hello and welcome to the session. In this session we discussed the following question which says, in the given figure x is to y is equal to 2 is to 3 and angle prs is equal to 120 degrees, find the values of x, y and z. Before moving on to the solution let's recall some important facts. We know that the sum of the angles of a triangle is 180 degrees and also if a 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 that we use in this question. Now we move on to the solution. In this figure we are given that x is to y is equal to 2 is to 3 and angle prs is equal to 120 degrees. We need to find the values for x, y and z. Now the side qr of triangle pqr is produced to s 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. This means that 120 degrees is equal to rqp which is x degrees plus qpr that is y degrees. Or you can say that x degrees plus y degrees is equal to 120 degrees. Let this be equation 1. Now since we have x is to y is equal to 2 is to 3 so we take let x be equal to 2t and y be equal to 3t. So substituting these values of x and y in equation 1 we get 2t degrees plus 3t degrees is equal to 120 degrees. Or you can say 2t plus 3t is equal to 120 which means that 5t is equal to 120 or t is equal to 120 by 5 and that is equal to 24. So therefore we get x is equal to 2t that is 2 into 24 that is equal to 48 and y is equal to 3t that is equal to 3 into 24 that is equal to 72. Now that we have got the values for x and y we need to find the value for z now. So for this we consider the triangle pqr in this angle pqr plus angle qrp plus angle rpq is equal to 180 degrees. Since the sum of the angles of a triangle is 180 degrees. So this means x degrees plus y degrees plus z degrees is equal to 180 degrees. Now we put the values for x and y so we have 48 degrees plus 72 degrees plus z degrees is equal to 180 degrees. This means we have z degrees plus 120 degrees is equal to 180 degrees. Or we can say that z degrees is equal to 180 degrees minus 120 degrees that is z degrees is equal to 60 degrees or we say z is equal to 60. So we have now got the values for x, y and z so we have x equal to 48, y equal to 72 and z equal to 60. This completes the session. Hope you have understood the solution for this question.