 Hello and welcome to the session. In this session we discuss the following question which says in a pentagon A, B, C, D, E, A, B is parallel to E, D and angle B is equal to 140 degrees. Find the interior angles C and D if angle C is to angle D is equal to 5 is to 6. We know that sum of the interior angles of a convex polygon of n sides is equal to 2n minus 4 right angles. This is the key idea that we use in this question. Let's move on to the solution now. This is the pentagon A, B, C, D, E. In this we are given that A, B is parallel to E, D and we are also given that angle B is equal to 140 degrees. Also we are given the ratio of angle C to angle D that is angle C is to angle D is equal to 5 is to 6 and we are supposed to find the interior angles C and D. Now since we are given that A, B is parallel to E, D. Therefore, angle A plus angle E is equal to 180 degree. Since we know that sum of the interior angles on the same side of the transversal is 180 degrees. Let this be result 1. Next we have angle C is to angle D is equal to 5 is to 6. Therefore, we can have angle C equal to 5x and angle D equal to 6x. Now consider this pentagon A, B, C, D, E. Let's see the sum of the interior angles of this pentagon. We have angle A plus angle B plus angle C plus angle D plus angle E. This would be equal to 2n minus 4 right angles according to the key idea. Now since this is a pentagon so it means it is 5 sides that is in this case n would be equal to 5 thus we get this is equal to 2 into 5 minus 4 right angles or you can say this is equal to 10 minus 4 into 90 degrees that is 6 into 90 degrees which is equal to 540 degrees that is we have angle A plus angle B plus angle C plus angle D plus angle E is equal to 540 degrees. Now further we get angle A plus angle E plus angle B plus angle C plus angle D is equal to 540 degrees. Now we know that sum of the angles A and E is equal to 180 degrees as in the equation 1. So this means we have 180 degrees plus now the measure of angle B is given as 140 degrees so we put the value of angle B as 140 degrees here. So 180 degrees plus 140 degrees plus angle C is 5x plus angle D is 6x is equal to 540 degrees that we have 320 degrees plus 5x plus 6x is 11x is equal to 540 degrees. Further 11x is equal to 540 degrees minus 320 degrees or you can say 11x is equal to 220 degrees. To get the value of x we divide both sides by 11 so 11x upon 11 equal to 220 degrees upon 11 11 cancels with 11 and 11 20 times is 220 therefore we have x is equal to 20 degrees but we had angle C equal to 5x which means this is equal to 5 into 20 degrees equal to 100 degrees and angle D equal to 6x equal to 6 into 20 degrees that is equal to 120 degrees. Therefore we have got the values of angle C and angle D final answer is angle C equal to 100 degrees and angle D equal to 120 degrees. This completes the session hope you have understood the solution of this question.