 Hello and how are you all today? My name is Priyanka. The question to be discussed is in figure 7.51, pr is greater than pq and ps bisect angle qpr. Prove that angle pr is greater than angle psq. Now this is the figure 7.51 which we need to refer. Let us proceed on with our solution. Here we are given that pr is greater than pq and angle 1 is equal to angle 2. Let us name these angles. Let this be angle 1, 2, 3, this be 4, 5 and 6. Right. Further we need to prove psr is greater than angle psq. That is angle 4 is greater than angle 5. Let us proceed on with the proof. Now one of the terms that we have learnt says that angles opposite to size larger side is greater. Right. Here we are given that in triangle pqr, pr is greater than pq. So we can say that angle 6 is greater than angle 3 because angles opposite to the larger side is greater. Since pr is the greater or the larger side, so angle 6 which is opposite to this side will be the greater. Further add to angle 1. To both sides we have angle 1 is greater than angle 3 plus angle 1 or we can say that angle 6 plus angle 1 is greater than angle 3 plus angle 2 because angle 1 is equal to angle 2 we are given in the question that ps is the bisector of angle. So angle 1 is equal to angle 2. Now in triangle p218 degree. So I have added all the angles of the respective and have equated to. The left and the right sides of these two equations are equal to each other. That means the left hand side will also be equal. So we can say that therefore angle 1 plus angle 6 plus angle 5 is equal to angle 2 plus angle 4 plus angle. Also we know that angle 1 plus angle 6 is greater than angle 3 plus angle 2. That means angle 1 plus angle 6 bear of these two angle is greater than these two angles. So automatically this side will be the greatest. These two sides are equal since they both are greater than this these two angles that means angle 5 will be comparatively greater than angle 4 so that these two equations can equate. So we can say that therefore angle 5 is less than angle. Here angle 5 is not greater than but it is less than angle 4 to equate it or we can say that angle 4 is greater than angle 5. And angle 4 is what? Angle PSR and angle 5 is angle PS. This is our required proof of the question. This ends the session. Hope you enjoyed and have a great day ahead. Bye for now.