 Hello and welcome to the session. In this session we discuss the final question which says SPT is a tangent to the circle at P and PQ is a part of the circle is and the PRQ is equal to 40 degrees and the PQR is equal to 80 degrees find X and Y. Let us first discuss the alternate segment property. According to this we have straight line is a circle from the point of contact a chord is drawn the angles between the tangent and the chord respectively equal to the angles. The alternate is the key idea that we would use in this question. If we want to the solution this is a figure given to us in which we have SPT tangent to the circle at the point P is the best circle where we have angle PRQ is of measure 40 degrees and angle PQR is of measure 80 degrees and we are supposed to find SPT is the tangent to the circle and PQ is the chord on the point of contact on the key idea that is the alternate segment property we have that if a straight line touches a circle and on the point of contact a chord is drawn when the angles between the tangent and the chord are respectively equal to the angles in the alternate segment. Therefore the QPT would be equal to its segment which is angle PRQ this is using the is equal to 40 degrees that is X is equal to 30 it is the tangent and PR is the chord so angle between the tangent and the chord which is angle would be equal to angle in the alternate segment that is angle PQR using the alternate segment this means angle SPR which is Y is equal to angle PQR which is 80 degrees that is we now have Y equal to 80 degrees. The answer is X equal to 30 degrees and Y equal to 80 degrees. This is the QPT solution of this question.