 Okay, friends, so I am a back end with another theorem and we are going to prove today that the sum of all the angles Round the point is equal to 360 degrees It's a knowledge which you have acquired, you know sometime back and now it's time to prove it So hence the question is or the statement is the sum of all the angles Round the point is equal to 360 degree. What does it even mean? So let's say I have a point P and There are lots of angles Which is let's say having a vertex P. Okay, so lots of angles are possible Yep, so lots of angles are possible with vertex P. So I'm just drawing drawing them Okay, so let's say like that. So there are lots of angles around point P Let's name them. So let's say this is a this is B. This is C D and E. Okay, how many angles five? Five angles are, you know, seen direct angles. There are many more angles. For example angle B P is also an angle, but then we are considering only these which one. So let's say this is X or let's say, you know some other names, let's say Yeah, let's say this is a small a this is B small b small c D and E. Okay, so you have to prove that A plus B plus C plus D plus E is always 360 degrees Okay, so if you add all the angles around the point, it will give you 360 degrees. How to prove that? Always remember whatever Knowledge we had or we have so far. We will be using that only to prove it. Now one way is you can just Do one thing and what is that? You can draw a straight line Straight line like that passing through point P and let's let's name them M and N Okay, now if you see a plus B plus C plus D plus E can be written as so if you see a itself A itself is a sum of let's say I am now naming it as a one and And a two two parts right so this PM rate divides angle a P e into two parts such that A is equal to some writing this here a is equal to clearly a one plus a two Similarly D. Let's say this is D one and this is D two So I can also write D is equal to D one plus D two Isn't it now? Let's Try to rewrite this statement. So hence this statement will become what will it become it means a can be written as a one plus a two Plus B plus C plus D one plus D two plus E Okay Right now I can club few of them. So let's say can I not club a C and D one so let me let me club like this. So this entire thing can be rewritten as C plus D one within brackets. So I have just picked these two up and written in the first place C plus D one plus B plus a two Okay, so this also I have clubbed together. So B plus a two then I'm writing D two Plus E so I am clubbing D two plus E together. So these two are also gone. What is left only a one Plus a one, right? If you look carefully the same thing is written over here Okay, now what C plus D one if you see C plus D one guys, what is C plus D one? So C plus D one is this angle and C is this angle. So C plus D one will be nothing but This whole angle. So hence I can write that is this directly is equal to angle B P N Is it and B plus a two if you see this is B This is B. This is a two. This is a two. So B plus a two is angle B P M Okay, now you write them together and then D two plus E. So if you see this is D two, this one is D two and This is E. So D two plus E is nothing but angle N P E and a one can be directly written as angle E P M and club them together as well Now, what is this if you see closely? This is a linear pair Isn't it ray OB stands on line MN and hence this is a linear pair and this is also a linear pair Which Ray row O E Stands over MN and hence this is also a linear pair. So hence you can write this as 180 degrees for this linear pair plus another 180 degrees for this linear pair Okay, so hence total is nothing but 360 degrees Okay, now this is what you have to prove it. Okay, so hence at any point. So, however how many numbers of Rays are there doesn't matter. So let's say this is Yep, these are all different Rays, okay, and On all originating from point same point So let's say this is one. This is two. This is three. This is four. This is five. This is six This is seven. So angle one plus angle two plus angle three plus angle four plus angle five Plus angle six plus angle seven will always be equal to 360 degrees Okay, you can think it think it in this way as well. So if you keep on adding a raise All the rays are like that keep on adding infinitely many rays if you add it will eventually make a disc Is it it will turn out to be a You know, it will form a Disc or a circle. So hence at the center the circle always makes 360 degrees angle is it okay. So this is what was the objective of this theorem I hope you understood this theorem and it's true