 In the given question It has been given that AB is parallel to CD and P is any point between the two lines Okay, so these two lines are parallel first of all and P here is a point Between the two lines you have to prove that ABP that is X Plus CDP that is let's say Y is equal to Bpb that is there, okay, so we have to prove This or you can say X plus Y is equal to Z Okay, again, so this is a case of two parallel lines and there are two Transversals if you see PB is one of them and You know it is produced. It is going to cut it like that, right? So but now what we are going to do is we are going to you know utilize the property of Parallel lines and transversals. So so we need to prove that Z is X plus Y So here we need to do a construction. So What construction shall we do? So let us draw a line past parallel to parallel to AB and CD but passing through P So we have done a construction here where a line. Let's say PQ is has been drawn to be parallel to AB and CD Okay, now this helps us a lot. Why because if you see now Z is Just Z has been broken down into two angles now if you see this one Okay, and this one Right Z is some of right. So can we say Z or this angle Z was nothing but angle Dpb Dpb Dpb is Z is equal to can I say this is angle B Pq plus angle Dpq Right, you can see Dpq plus Dpq sums the sum comes out to be Z. Okay Now if you look carefully a B is parallel to Pq. That's why construction Okay, so hence can I say X is equal to angle B Pq why the reason is alternate interior angles Similarly CD is parallel to Pq, right? So we had drawn drawn Pq parallel to AB and AB was parallel to CD So we had drawn Pq parallel to AB and AB was parallel to CD given Right that means Pq is also parallel to CD, right? So we are using that here and from here you can say angle Qpd is equal to y again same reason alternate interior angles Now guys if you see Z, let's say this was one so one two and three so from one two three What can we say we can replace Bpq by X and Dpq or Qpd by Y. So hence we can say Z is equal to Bpq first and what was Bpq X. So it is X Plus Dpq or Qpd. What was that? Y. So hence proved hence proved