 In this question, it's given that A, B, C, D and EF are three parallel lines, okay, and Y is to Z, so Y and Z are two angles, you can see this is Y here, this is Z here, so Y and Z are in the ratio 3 to 7, you have to find the value of this angle X, okay, so let's solve this question, so if Y is Z, Y is to Z is 3 to 7, so first of all you see you can see that this angle is also Y because this is vertically opposite angle, so hence if I name this point O, so let's say angle POC is equal to angle QOD, QOD which is actually equal to Y, okay, now Y plus Z is equal to 180 degrees, yeah, so approach to such problems is one is the given fact, now that is 3 to 7, another thing is how can we relate, you know, these two Y and Z, so another relation is Y plus Z is 180 degree Y because adjacent angle, adjacent angles, right, are supplementary in parallel lines, so adjacent angles are supplementary, you know, along a transversal, you know that the Y and Z are adjacent angles and then Y plus Z should be 180 degrees, now from the given fact we know that Y upon Z is 3 by 7, so what can I say about Y, can I not write this as Y is 3 by 7 Z, this is one way of doing it, another way of doing it is let's say Y is equal to 3X, no not X, so X is being used here, so let's say 3K and Z is equal to 7K, this is how many people also try substituting like this but then I prefer this method, so Y is equal to 3 by 7 Z, now this you name it as 1 and this you name it as 2, so using 1 and 2, what do we get, so I can replace Y, this Y I can replace, no, so by what, by this, so hence I can write 3 upon 7 Z plus Z is 180 degrees, right, so hence if you take LCM you'll get 3 Z plus 7 Z divided by 7 is 180 degrees, so this implies 10 by 7 Z is equal to 180 degrees, so what is Z guys, Z will be 180 degrees into 7 upon 10, right, so it is 126 degrees, okay, so what is Z, Z comes out to be 126 degrees, okay, now what, so if Z is 126 degrees that means what, now see this or let me just do it here, right, so now we can say AB is parallel to EF also it's given, that means angle A, let me call this point as M and N, so angle AM, AMN is equal to angle A, N, M and why so, this is because alternate interior angles are equal, okay, so what is AMN guys, AMN is nothing but X and what is A, N, M, A, oh I'm sorry, this should not be A, M, N, N, M, N, F, N, M, so my bad, this is F, N, M, F, N, M, right, AMN and F, F, N, M, so hence this is nothing but X is equal to Y, sorry not Y, X is equal to Z and we found out that Z was 126 degrees, so hence X also is 126 degrees and that should be the answer, okay,