 Hello and welcome to the session. In this session we will discuss interior and exterior angles of a polygon. Consider this polygon A, B, C, D, E, F. This polygon as you can see, these are the interior angles of the polygon. That is we have angle A, F, E. That is this angle, angle F, E, D. This angle, angle E, D, C. Then angle D, C, B, angle C, B, A. That is this angle. These are the interior angles of the polygon. And from this figure we find that angle is C, exterior angle of the polygon. Consider this convex polygon A, D, C, D, E, and so on, N sides. Now we consider a point A with this polygon and join each vertex of this polygon. With this point O, see on joining this point O with each vertex of the convex polygon, we would get triangle A, B, triangle O, B, C, triangle O, C, D, triangle O, D, E and so on. The sum of the angles triangle will be equal to right angles. Or you can say 180 degrees since one right angle is 90 degrees. So 2 into 90 degrees is 180 degrees. Which means that if you consider this triangle A or B, then sum of the angles of this triangle would be equal to 180 degrees. There are N triangles found. So the sum of would be equal to, 180 degrees into N. Now the sum of the angles formed implies that the interior angles to polygon these angles at the point O be equal to right angles. Int O is equal to or you can say 360 degrees. Therefore you can say that sum of the interior angles polygon would be equal to minus the sum of the angles at the point O which is right angles. And so this would be equal to 2 N minus 4 equal to right angles. This is the sum of the interior angles of the polygon. Thus we have a statement which says that the sum of the interior angles to convex polygon discuss about the exterior angle of the polygon we produce B, C, D, D, E, convex polygon A, B, C, D, E. This figure the side A, B of the polygon is produced to P, B, C is produced to Q, C, D is produced to R, D, E is produced to S and so on. But from the figure you can see that at each vertex the sum of the interior angle and the exterior angle would be equal to right angles. There are the adjacent angles on a straight line that is to form a linear pair. Like if you consider the vertex B then at this point B the interior angle which is angle AB2 plus the exterior angle which is angle PV2 would be equal to 2 right angles which is same as 180 degrees. Now on multiplying both the sides by N we have N into interior angle plus N into exterior angle is equal to shown that the sum of the interior angles of a convex polygon of N sides is 2 N minus 4 into right angles. We can write for the whole N into which is the sum of the N interior angles of a convex polygon is equal to right angles which is equal to right angles that is the sum of the N exterior angles is equal to 4 right angles. Thus we can now say that if the sides of the convex polygon are produced in order then the sum of the exterior angles right angles. The sum of the exterior angles of a convex polygon is always 4 right angles be whatever the number of sides of the polygon. The interior angles of the polygon is 2 N minus 4 the whole N into right angles this can also be written as N minus 2 the whole N into 180 degrees. So we can also say that the sum of the interior angles of a convex polygon or say N sides would be given by N minus 2 the whole N to 180 degrees. Now if we have a regular polygon each interior angle regular polygon of N sides would be equal to 2 N minus 4 the whole upon 4 this one into right angles. The polygon all the angles are equal and we know that sum of the interior angles of a polygon is given by 2 N minus 4 the whole into right angles. So from this we conclude that each interior angle would be equal to 4 the whole upon N which is the number of sides of the polygon into right angles. In the same of a polygon is 4 right angles of a regular polygon which all the angles are equal each exterior angle would be equal to 4 upon N which is the number of sides of the regular polygon into right angles. We can also conclude that a regular polygon see degrees upon the number of sides of the polygon the interior angle would be given by 180 degrees minus exterior angle. So as we know that at each vertex of the polygon the interior angle and the exterior angle is equal to 180 degrees. In this session hope you have understood the concept of the interior and the exterior angles of a polygon.