 Hi and welcome to the session. I am Priyanka and let us discuss the following question. It says in figure 7.48 sides AB and AC of triangle ABC are extended to point P and Q respectively. Also angle PVC is less than angle QCP. Show that AC is greater than AB. Now this is the figure 7.48 which we need to refer. We are given that this angle is less than this angle. Let us name these angles as angle 1, angle 2, angle 3 and angle 4. So it's given to us in the question that angle 1 is less than angle 2. So we need to prove that AC is greater than AB. Let us start with our proof. Now in triangle ABC we can write that angle 1 plus angle 3 is equal to 180 degrees because they are forming a linear pair. Similarly angle 2 plus angle 4 is equal to 180 degrees because of the same reason. So we can say that therefore angle 1 plus angle 3 is equal to angle 2 plus angle 4 since both of these sums are equal to 180 degrees. Also angle 1 is less than angle 2. It's given to us. So this means that angle 3 will be greater than angle 4, isn't it? Let us take an example. It is saying that angle 1 is less than angle 2. Let's say angle 1 is 80 degrees and angle 2 is 100 degrees. Then angle 3 will be 100 degrees and angle 4 will be 80 degrees since they all are equal to 180 degrees. So this means angle 3 is greater than angle 4. Now if you see in the question the side opposite to angle 3 is AC. So therefore AC is greater than AB. Mentioning the reason that because side opposite to greater angle is larger. So this completes the question that was given to us. I hope you enjoyed the session. Bye for now.