 Hello and welcome to the session. I am Asha and I am going to help you solve the following question which says the angles of a quadrilateral are in the ratio 3 is to 5 is to 9 is to 13 find all the angles of the quadrilateral. So let us begin with the solution and let A B C D B the required quadrilateral then we are given that the angles of the quadrilateral are in the ratio 3 is to 5 is to 9 is to 13. This implies angle A is equal to 3x, angle B is equal to 5x, angle C is equal to 9x and angle D is equal to 13x. So in the figure angle A is 3x, angle B is 5x, angle C is 9x and angle D is 13x where x is a positive real number and x is greater than 0. Now as we know sum of 4 angles of a quadrilateral is equal to 360. So this implies angle A plus angle B plus angle C plus angle D is equal to 360 degree that is 3x plus 5x plus 9x plus 13x is equal to 360. This further implies that 30x is equal to 360 or x is equal to 360 upon 30. So in cancelling we have 312s are 36. So we have 12 degrees that x is equal to 12 degrees. So this implies angle A is equal to 3x which is equal to 3 into 12. So angle A is 36 degree, angle B is 5x. So 5 into 12 is 60. So angle B is 60 degree, angle C is 9x. So we have 9 into 12 which is equal to 108 degrees and lastly angle D which is equal to 13x. So we have 13 into 12 which is equal to 156 degree. Therefore 36 degree, 60 degree, 108 degree and 156 degree are the angles of the quadrilateral. So this completes the session. Take care and have a good day.