 Hello friends, welcome to another session on geometry and in this session we are going to discuss another attribute of the triangle and that is the exterior angle to a given triangle So you can see in this figure. There's a triangle ABC right and What I have done is I have just extended all the sides in both the directions, right? so you can see AB this is the line AB segment line segment AB and N and M represent the points on the extended line F, right? similarly B and C are Joined as in the side of the triangle and B and C are extended both sides L and O are the points on that line, right and A and what? C AC right extended both sides K and J are the points on that line So that is what I have done in this case. Now How do we define in exterior angle? So you can see alpha beta gamma delta and Epsilon and jita there are these are six angles, which you can see which all are they so mbc Lba Kab NAO Sorry NAC and Then OCA and JCB all these are exterior angles. So how many there are? Six exterior angles now clearly these Vertically opposite to the internal angle that is this is internal angle is it BAC interior angle now Vertically opposite to that internal angle that is this KAN is not considered as extra exterior angle So for exterior angle you must have one side of the triangle and One extended side of You know one extended side of the other side of the triangle called it So one side has to be there so AB has to be there now if you're picking up this side Then any of the extended sides that is a K is the extended side of AC. So so the two arms will be One of them will be the one of one side of the triangle and the other arm of that triangle has to be the Extended arm of the same Triangle, but some other some other arm not the same previous arm. I hope you got it So in case this is BC is the arm correct BC is one of the arms of the or one of the sides of the Triangle now this if you are taking this then there are two possibilities one extended arm is AB which goes to M so if you take that as one of the arms of the angle so mb is one of the arm and BC is one of the arms so angle formed by them here in this case alpha is called exterior angle similarly LB a where AB is the side of the triangle and BL is extended side CB, right? So these are two Exterior angles like clearly LB M is not an exterior Why because the either of the two or both of the two are not having or Not any of the sides of the triangle right so neither BL nor BM So BL nor BM is the side of the triangle. So hence this angle will not be counted as an exterior Angle to the given triangle ABC got it. So once again exterior angle of any given triangle will be nothing but the angle formed by one of the sides of the triangle and And One extended side of any of the other two sides, right? So don't count this one. So this one is counted for the exterior angle Then the other arm of that exterior angle will be the extended arm of the other side of the triangle that is BC extended gives you CO is one of the arm and AB or sorry AC is the other arm. So ACO becomes the exterior angle now you can also See that The two pairs of exterior angle are equal and rightly so because they are pair of vertically opposite Angles, so they have to be equal. So in a nutshell, we can say that in a triangle, there are three pairs of Exterior angles right three pairs of equal exterior angles So alpha beta is one pair and then this epsilon and jeta is another pair 129.89 degrees here in this case and Delta and gamma are another pair so six pairs or sorry three pairs or six exterior angles are possible in the triangle Now I will just try to move this point be and show you that It is very much Valid for any case. So see I'm changing the location of B so in any case there are three or you're getting three pairs and three pairs of exterior angle or Six exterior angle right and see that guys. So you will get always three pairs of exterior angle and in every case The three pairs are equal in every case The opposite pairs, you know, they are equal. So whether it is AB or C, whichever I extend wherever I take you will always get Three equal pairs of exterior angles I hope you understood the concept of exterior angles. Now we will be studying some theorems related to exterior angles of