 Hello and welcome to another problem-solving session guys. So in this session we are going to take up this question which says that if in the given figure triangle EDC and EBA. So check triangle EDC. So EDC. So this is the triangle they are talking about EDC and EBA. EBA are similar. Okay, so let me remove these lines so that Yeah, it's clear, right? So these these are the two similar triangles. BEC is given to be 115 degrees C and EDC is 70 degrees C. So find out DEC. So all these angles are to be found out. So this angle X and Let me use another color to write this. So this is X Then what? DCE. DCE. So let this be Y. So we have to find out Y. What else? EAB. EAB. Let this be Z. Z. AEB. AEB. Let this be U and EBA. EBA. Let this be V. Okay, so let's now prove and find basically. So there are a few things which are clearly understood. That is X is equal to U because of vertically opposite angles. But let's start with this given thing. So triangle EDC is similar to triangle EBA. EBA. Okay, so this is given. So that means what? Corresponding angles will be equal. So angle E is angle E anyways. So angle D is going to be equal to angle B. Correct. Angle D is going to be angle B. So hence angle EDC is going to be equal to angle EBA. And EDC if you see in the figure it's 70 degrees. So EBA is 70 degrees. So hence we get V. Angle V is equal to 70 degrees. First one done. Okay, now similarly you can say now you can say in triangle, see in triangle EAB. EAB. So if you see 115 degrees in external angle, right? So angle BEC is equal to, if I write BEC, this is equal to Z plus V. And why is this? This is because of external angle is equal to sum of interior opposite angles. Isn't it? Interior opposite angles, right? So sum of interior opposite angles. So hence now V already I know that is 70, BEC is given that is 115. So I can write 115 degrees is equal to Z plus 70 degrees. Isn't it? So clearly angle Z is equal to 115 degrees minus 70 degrees which is nothing but 45 degrees. So Z becomes 45 degrees. Okay, Z is 45 degrees, no problem. So DCE is or sorry BAE. BAE is right. So hence we have completed this as well. So EAB. So this is angle EAB. Let me write this as EAB. And what else did we find out? EBA. So this is also done. So these two are done. Now since again, let's use the similarity. Since DCE triangle EDC is similar to triangle EBA. Therefore, what do we get? We can say angle C, right? That is angle ECD is equal to angle EAB and that is equal to Z and that we found out is equal to 45 degrees. Correct? So Y also is now known. Y is 45 degrees, right? So what was Y by the way? EAB. So we are done with, sorry, ECD, right? So DCE, this is also done. Okay, now what? X and U only have to be found out. So clearly X is nothing but 180 degrees minus 70 degrees minus Y which is 45 degrees, and why is this? Angle some property guys. So this is because of angle some property of triangle. So that means X is clearly 180 minus 70 is 110. 110 minus 45 is 65 degrees. So we get X as 65 degrees and this will be equal to U as well. Why? Because of vertically opposite angles, right? So DCE and sorry DEC, DEC is done and AEB is also done. Both are same. So AEB and DEC both are 65 degrees. So all set, right? So I hope you understood this problem. So it was a very simple problem. We had to invoke some of our knowledge of previous grades of triangle some, angle some property of a triangle and external exterior angle is equal to sum of interior opposite angles. So these things you must remember. And using that and the concept of similarity, we could achieve the results.