 Okay friends so in this question AB is given to be parallel to CD okay so this is given and angle F here is 30 degrees so this angle is 30 degrees and we have to find ECD which we have expressed as X also from the figure it is clear that FA is perpendicular so it is 90 degree here okay so let's try and find out so we have to find out X so let's do you know reverse thinking that is what should we do to find X so if you see if I somehow know this angle then we are done because let's say this angle is Y so Y plus X has to be 180 degree Y because AB is parallel to CD and they happen Y and X happen to be adjacent angles okay now if this angle is Y then clearly this angle has to be Y because vertically opposite angles and if I know 30 degrees and 90 degrees I know Y in triangle AFE and I think we are done so we'll write in triangle AFE right angle AFE plus angle FAE plus angle AEF is equal to 180 degrees and the reason is angle some property of a triangle angle some property of a triangle that says that sum of three angles of a triangle is 180 degree now AFE is given to be equal to 30 degrees AFE is given to be equal to 90 degrees and AEF is Y and this is 180 degrees so my dear friends Y will be 180 degrees minus 30 degrees and minus 90 degrees which is equal to 60 degrees okay so Y is now known also you can say X plus Y is 1 sorry not 120 180 degrees Y adjacent angles adjacent angles right are always in in case of parallel line and a transversal cutting them the adjacent angles must be equal to 180 degrees or adjacent angles are complementary so you will get X from here which is 180 degrees minus Y which is nothing but 180 degrees minus 60 degrees which is equal to 120 degrees okay this is one way of doing it do we have another method to solve the same question yes we do have see what you could have done is we could have you know just drawn a line like that okay which is parallel to AF let's say this line is parallel to this line so what will happen if this is 30 degrees then this also is 30 degrees alternate interior angles and if that is 30 degrees this angle has to be 30 degrees particularly opposite angles and if this was 90 so this angle also has to be 90 if they're parallel so that means this angle is also 90 degrees so this whole is 90 and this is 30 so hence eventually hence it should be 60 degrees so this is another way of solving so the same problem could be solved once you know in multiple ways once again what did I do in this case is I just drew a line parallel to AF let it be PQ okay PQ is PQ is parallel to AF the moment that is done so this 30 degree and this 30 degrees they are same why alternate interior angles so if this is 30 degrees then this angle has to be 30 degrees let me use this color to depict it 30 degrees why because of vertically opposite angle CF and PQ these are the two lines intersecting let's say at E so 30 30 now this is 30 and entire Q EB this entire thing was 90 right why because this was 90 again by vertically opposite angle so the total is 90 and this angle is 30 then the remaining has to be 60 so hence you could have solved like this as well so there are multiple ways of solving the same problem