 Hello and welcome to this session. In this session, we will discuss polygons. A simple closed curve made up of only line segments is called a polygon. Consider this figure. This is a polygon since it is a closed curve which is made up of only line segments. But this figure is not a polygon since it is not closed. Now let's discuss classification of polygons. We classify the polygons according to the number of sides or vertices they have. This is how we classify the polygons. Like if the number of sides or vertices of a polygon are three then it is called a triangle and this would be the figure. And if the number of sides or vertices are four then it is a quadrilateral of this kind. With five number of sides or vertices it is a pentagon which is of this kind. With six number of sides and vertices it is a hexagon and the figure would be of this kind. And if we have seven number of sides or vertices then it is a heptagon and the figure would be of this kind. Now let's discuss diagonals. Basically a diagonal is a line segment connecting two non-convegative vertices of a polygon. Like for this polygon A, B, C, D, A, C and B, D are the diagonals. A, C is formed by connecting the non-convegative vertices A and C and B, D is formed by connecting non-convegative vertices B and D. Consider this closed curve. Now this portion is the interior of this closed curve and this portion is the exterior of the closed curve. Next we discuss convex and concave polygons. Polygons which have no portions of their diagonals in their exteriors are called convex polygons. For example consider this figure. This is a convex polygon since if we join the non-convegative vertices to get the diagonals we see that all the diagonals are in the interior of this polygon. None of the diagonals are in the exterior. So this is a convex polygon and the polygons which have some portions of their diagonals in their exteriors are called concave polygons. Like if you consider this figure and you make the diagonals in this figure by joining the non-convegative vertices you see that this diagonal lies in the exterior of the given figure. So we say that this is a concave polygon. Next we shall discuss regular and irregular polygons. Basically a regular polygon is both equiangular that is all the angles of that polygon are equal and equilateral that is all the sides are also equal. Like this square has all the sides equal and all these angles are 90 degree and hence equal. So this is a regular polygon and a polygon which is not regular is called irregular polygon. This is a rectangle in which the opposite sides are equal. So this is not equilateral and hence we say that it is irregular polygon. Now we discuss angles and property. We know that the sum of the three angles of a triangle is 180 degrees. This is the angles and property of a triangle. Now the sum of the measures of the four angles of a quadrilateral is 360 degrees. This is the angles and property of a quadrilateral. Consider this quadrilateral ABCD in which we have angle A is 130 degrees, angle B is 120 degrees, angle C is of measure x and angle D is 50 degrees. We need to find the angle measure x. According to the angles and property of the quadrilateral we have that the sum of the measures of the four angles is 360 degrees. So angle A plus angle B plus angle C plus angle D is 360 degrees that is 130 degrees plus 120 degrees plus x plus 50 degrees is equal to 360 degrees. So from here we get x is equal to 360 degrees minus 300 degrees which is equal to 60 degrees. So angle C is equal to 60 degrees. Now we discuss sum of the measures of the exterior angles of a polygon. We have that the sum of the measures of the external angles or you can say the exterior angles of any polygon is 360 degrees. Consider this polygon ABCD in which we are given the measures of the external angles of this polygon. So according to this property we have 70 degrees plus 70 degrees plus 110 degrees plus x would be equal to 360 degrees from here we have x is equal to 110 degrees. So this completes this session. Hope you have understood the concept of polygons.