 Hello and welcome to the session. In this session we discussed the following question which says in the given figure PQ is parallel to RS angle PQO is equal to 100 degrees, angle ORS is equal to 120 degrees and angle QOR is equal to X degrees. Find the value of X. We know that if two parallel lines are intersected by a transversal, then the sum of the consecutive interior angles is 180 degrees and we also know if a ray stands on a line, then the sum of the adjacent angles so formed is 180 degrees. This is the key idea to be used in this question. Let's move on to the solution now. This is the figure given to us in which we have PQ is parallel to RS angle PQO is equal to 100 degrees, angle ORS is equal to 120 degrees and angle QOR is equal to X degrees and we need to find the value for X. First of all we draw AOB parallel to PQ parallel to RS. So this AOB is parallel to PQ and also parallel to RS. That is we have AO is parallel to PQ since AOB is parallel to PQ and here we have OQ is the transversal. So since we know that if two parallel lines are intersected by a transversal, then the sum of the consecutive interior angles is 180 degrees. So as AO is parallel to PQ and OQ is the transversal, therefore the sum of the consecutive interior angles that is angle PQO plus angle QOA is equal to 180 degrees. Now angle PQO is equal to 100 degrees. So this gives us 100 degrees plus angle QOA is equal to 180 degrees which further gives us angle QOA is equal to 180 degrees minus 100 degrees and this is equal to 80 degrees. So we have got angle QOA equal to 80 degrees. Now next we consider RS parallel to OB since AOB is parallel to RS also. So we can take RS parallel to OB and here OR is the transversal. Therefore since we know that if two parallel lines are intersected by a transversal, then the sum of the consecutive interior angles is 180 degrees. Thus using this result we would get that angle SRO plus angle ROB is equal to 180 degrees. Now SRO or you can say ORS is given as 120 degrees. So 120 degrees plus angle ROB is equal to 180 degrees. So this gives us angle ROB is equal to 180 degrees minus 120 degrees that is equal to 60 degrees. So we have got angle ROB as 60 degrees. Now since we know that if a ray stands on a line, then the sum of the adjacent angles so formed is 180 degrees and we know that AOB is a straight line and here OQ and OR are the rays standing on it. So this means that the sum of the adjacent angles so formed is 180 degrees that is angle QOA plus angle QOR plus angle ROB is equal to 180 degrees. So this means 80 degrees since angle QOA is of measure 80 degrees plus X degrees that is angle QOR which is X degrees plus angle ROB which is of measure 60 degrees is equal to 180 degrees that is we have 140 degrees plus X degrees is equal to 180 degrees which means that X degrees is equal to 180 degrees minus 140 degrees that is equal to 40 degrees. Thus we get X is equal to 40. Thus X equal to 40 is our final answer. This completes the session. Hope you have understood the solution for this question.