 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says, in figure 6.42 if lines PQNRS intersect at a point T such that angle PRT is 40 degree, angle RPT is 95 degree and angle TSQ is 75 degree, find angle SQT. So we have to find angle SQT which is this angle. Let us now begin with the solution and in triangle PRT, sum of angles PRT, angle TPR is equal to 180 degree since sum of 3 angles of a triangle is equal to 180 degree which is the angle sum property of your book. Now angle PRT is 40 degree this is given to us plus angle RTP we will find out and angle TPR is 95 degree which is equal to 180 this implies 40 plus 95 is 135 degree plus angle RTP is equal to 180 degree which further implies that angle RTP is equal to 185 degree minus 135 degree which is equal to 45 degree. Therefore we have angle RTP is equal to 45 degree let this be equation number 1 so this angle is 45 degree. Now since PT and RS are 2 lines which intersect at a point T this implies angle PTR is equal to angle STQ and so angle STQ is also equal to 45 degree. Let us write down PQ and 9RS intersect at a point T this implies angle PTR is equal to angle STQ since they are vertically opposite angle PTR is 45 degree this is equal to angle STQ so this implies that angle STQ is equal to 45 degree let this be equation number 2. Now let us see in triangle STQ here we have 2 angles and we have to find the third one so applying the angles on property in triangle STQ we have angle STQ plus angle TQS plus angle QST is equal to 180 degree and angle STQ is 45 degree plus angle TQS we have to find out plus angle QST is 75 degree this is equal to 180 degree which further implies 120 degree plus angle TQS is equal to 180 degree or angle TQS is equal to 180 degree minus 120 degree which is equal to 60 degree thus we can say that angle TQS which can also be written as angle SQT is 60 degree so this concludes the solution hope you enjoyed it take care and have a good day.