 Hi and welcome to the session. Today we will learn about exterior angle of a triangle and its property. First you will find out how an exterior angle of a triangle is formed. Here we have a triangle A, B, C. Now an exterior angle of a triangle is formed when a side of a triangle is produced. So suppose we produce the line B, C like this and let us name the point D over here. So here angle A, C, D is in the exterior of triangle A, B, C. So this is the exterior angle of triangle A, B, C formed at vertex C. Now angle A, C, B of triangle A, B, C is an adjacent angle to the exterior angle A, C, D. And the two remaining angles of triangle A, B, C that is angle A and angle B are called interior opposite angles of angle A, C, D or remote interior angles of angle A, C, D. Now at each vertex of a triangle say A, B, C there are two ways of forming exterior angle. That is if we produce side B, C of triangle A, B, C then at vertex C angle A, C, D is an exterior angle. And if we produce side A, C then angle B, C, E is an exterior angle at vertex C. Now let's say an important property related to exterior angle of a triangle. This states that an exterior angle of a triangle is equal to the sum of its interior opposite angles. Now here we have triangle A, B, C and we have produced the side B, C of triangle A, B, C. So here angle A, C, D is an exterior angle of triangle A, B, C. So according to this property we have angle A, C, D is equal to the sum of its interior opposite angles that is angle A plus angle B. Now let's see how we get this. Here we have from line segment C, E parallel to V, A is parallel to AC. AC's transversal that means angle A is equal to angle A, C, E as they are alternate angles. So we get angle A is equal to angle A, C, E. Again A, B is parallel to AC and V, D is transversal that means angle B will be equal to angle E, C, D as they are corresponding angles. So here we have angle B is equal to angle E, C, D. Now adding these two we get angle A plus angle B is equal to angle AC, E plus angle E, C, D. Now angle AC, E plus angle E, C, D is equal to angle AC, D that means angle A plus angle B is equal to angle AC, D. Thus this implies that the exterior angle AC, D is equal to the sum of its interior opposite angles that is angle A and angle B. Now this relation between an exterior angle and its two interior opposite angles is known as now next topic is angle some property of a triangle. The total ratio is 180 degrees of angle P, angle Q and angle R that is the three angles of the triangle P, Q, R will be equal to 180 degrees. Now let's see how we get this. Now suppose we name the angles of this triangle as angle 1, angle 2 and angle 3. Now let us extend the side Q, R. So here angle 4 is the exterior angle of triangle P, Q, R. Now by the exterior angle property of a triangle we get that the exterior angle that is angle 4 is equal to the sum of interior opposite angles that is angle 1 and angle 2. So angle 4 is equal to angle 1 plus angle 2. Now let us add angle 3 on both the sides. So we get angle 4 plus angle 3 is equal to angle 1 plus angle 2 plus angle 3. Now angle 4 and angle 3 form a linear pair. So that means angle 4 plus angle 3 is equal to 180 degrees. So let us replace angle 4 plus angle 3 by 180 degrees. We get 180 degrees is equal to angle 1 plus angle 2 plus angle 3. Thus this implies that sum of three angles that is angle 1, angle 2 and angle 3 of a triangle P, Q, R is equal to 180 degrees. Now let us take an example. We have given a triangle A, B, C, D is equal to 120 degrees is an exterior angle. Angle B is given to be 50 degrees and we need to find the values of X and Y. Now here angle A, C, D is an exterior angle. So by the exterior angle property of a triangle we know that angle A, C, D will be equal to angle A plus angle B. That is the sum of interior opposite angles substituting the values we get. Angle A, C, D that is 120 degrees is equal to angle A that is X plus angle B that is 50 degrees. So this implies X is equal to 120 degrees minus 50 degrees which is equal to 70 degrees. So here X is equal to 70 degrees. Now in triangle A, B, C using the angle sum property of a triangle we have angle A plus angle B plus angle A, C, B is equal to 180 degrees. Substituting the values we get 70 degrees plus 50 degrees plus Y is equal to 180 degrees. That means Y is equal to 180 degrees minus 70 degrees minus 50 degrees which is equal to 60 degrees. Thus the value of Y is equal to 60 degrees. Thus in this session we have learnt about exterior angle property of a triangle and angle sum property of a triangle. With this we finish this session. Hope you must have understood all the concepts. Goodbye, take care and keep smiling.