 Hello friends, welcome to this problem solving session on triangles. In this question, it's given that angle A is 100, though it doesn't look like it is 100 degree, but let me say this is 100 degrees. So, it is 100 degrees and A B is equal to A C. So, this side is equal to A C. You have to find B and C. So, this X and this Y. So, what are these? We have to find So, how to go about this? So, we just learned that angles, angles opposite to opposite to equal sides in a triangle, in a triangle are equal and vice versa right are equal and vice versa. Vice versa means that if angles are equal, the sides will be equal. So, if angles are equal, then sides are going to be equal. So, we know that X is equal to Y. So, we can say X is equal to Y. Now, X plus Y plus 100 degrees is equal to how much? 180 degrees and why is this? This is because of angle some property, angle some property of a triangle. Angle some property of a triangle is what we have learned. So, that means I can use these two equations, equation number one and equation number two to solve my problem here. So, it is 2X plus 100 degrees will be equal to 180 degrees. Very, very simple. So, 2X will be equal to how much? 180 minus 100, clear? 180 degrees minus 100 degrees. Correct? So, this is nothing but 80 degrees, right? 80 degrees. So, hence X will be simply 80 degrees by 2. So, we have proved or you have found out that X and Y both are equal to, right? So, hence angle B is equal to angle C is equal to 40, right? So, I hope you understood. So, here we have used two concepts. One is this, the concept that angles opposite to equal sides opposite to equal angles are equal and devices also and angles some property of a triangle. That is all, one more problem. So, here is one more problem guys. It says that in the given figure AB is equal to AC. Again, the sides are equal. These sides are equal and ACD is 120. So, you can check this is 120 degrees here. You have to find out angle A, correct? So, again the given the sides are equal. So, you have to write like this. What is given? AB is equal to AC, right? And what else is given? Angle ACD is equal to 120, isn't it? So, this is given. Now, what to find? You have to find what? You have to find angle A, okay? So, let us find that out. So, what is the use of this? You already know. So, we know that if AB is equal to AC, we know that. So, let us write the solution here. You know that since AB is equal to AC. Therefore, angle ABC is going to be equal to angle ACB, right? Because angles opposite to equal sides are going to be equal. So, let us say this is X, this is Y, right? And in fact, if it is X, this is X itself. So, I can write this as simply as X, isn't it? This is X. Now, so, I can write it here. Now, Y, angle sum property, angle sum property, angle sum property of a triangle. What can I say? Y angle sum property of a triangle, X plus X plus angle A, okay? X plus X plus angle A is going to be equal, isn't it? Y angle sum property of a triangle. So, hence, 2X also, we also have one more relationship, angle X plus angle A is 120 degrees. And why is that? This is exterior angle property, isn't it? So, exterior angle is equal to sum of what? Interior opposite angles I am writing in short, right? So, hence, I can find out these two relations are there. Now, let us, so first of all, let us simplify this one. So, we can write this equation here as 2X plus angle A is equal to 180 degrees, okay? And now, can I not write it here? So, let me write from this equation. Which equation? From this equation, I can write X is 120 degrees minus angle A, correct? So, 2X will be how much? 240 degrees minus 2 angle A, multiplying the entire equation by 2. We will get the same thing. Now, if this is true, then what can I say from this equation now, 2X plus A is 180. So, you can write 240 degree minus 2 angle A. Here, this one plus this angle A plus angle A is 180 degrees, right? I am using this equation now. So, from here, you will get angle A is equal to 60 degrees. 60 degrees. The angle A comes out to be 60 degrees. In fact, if angle A is 60 degrees, if this is 60 degrees and X and X are all, these are angle B is equal to angle C. So, X also is 60 degrees. You can calculate and this also will be 60 degrees. Okay. So, this is how we have to solve this problem. So, what are the underlying concepts here? So, we use two concepts. One is ASP, angles and property and another is exterior angle curve, right? We just learned in the previous chapter, right? So, I hope you understood this problem.