 Hello and welcome to the session. In this session we will discuss a question which says that the ferris wheel shown has 26 find the other and magnitude of symmetry of ferris wheel if seat 1 is rotated by 162 degrees, which seat of the position will it now occupy? Now let us start with the solution of the real question. Now we know if a figure is rotated less than 360 degrees about a point so that the image and the pre-image become indistinguishable, then the figure has rotational symmetry. Order of rotational symmetry is the number of times a figure is rotated so that it has rotational symmetry. Now here we are given a ferris wheel and this ferris wheel has 20 seats rotated in a circle. Now here we see the seat 1 is rotated by a certain angle, then we attain the first rotational symmetry at position 2, second at position 3, third at position 4, continuing this way, we will attain the 19th rotational symmetry at position 20 and 12th rotational symmetry will be attained when we move from position 20 to position 1. So there are 20 ways in which rotational symmetry is achieved thus order of rotation is equal to 20. And now we will find the magnitude that is angle of rotation which is equal to 360 degrees upon order of rotation and this is equal to 360 degrees upon 20 which is equal to 18 degrees we rotate at an angle of 18 degrees to attain rotational symmetry. Now if seat 1 is rotated by 160 degrees then we have to find its new position. Now we know that angle of rotation is 18 degrees so we reach a new position after every 18 degrees rotation. Now in 18 degrees we reached from seat 1 to seat 2 that is from 1 to 2 in next 18 degrees we reached from seat 2 to seat 3 Similarly in next 18 degrees we reached from seat 3 to seat 4 then next from seat 4 to seat 5 and going along this way we have reached from seat 9 to seat 10 that is in order 1, 2, 3, 4, 5, 6, 7, 8 and 9 that means in order 9 we rotate angle 9 into 18 degrees which is equal to 162 degrees and we reach at position of seat 10 it means if seat 1 is rotated by 162 degrees then the new position is 10. Now let us find this by calculation here the rotation is of 162 degrees now number of rotational symmetries attained in rotating 162 degrees is equal to 162 upon 18 which is equal to 9 Now here the seat 1 is rotated by 162 degrees and we have to find its new position now for total rotation of 162 degrees we have obtained order is equal to 9 Now from seat 1 to 2 the order is 1 then from seat 2 to seat 3 and then from 3 to 4 order is 3 then from 4 to 5 then from 5 to 6 order is 5 from 6 to 7 then from 8 to 9 order is 8 we reach position 10 seat 1 is rotated by 162 degrees then its new position is seat 10 So this is the solution of the given question that is all for this session hope you all have enjoyed the session