 Hello and welcome to the session. In this session we will discuss the question which says that pre-image and its image are 232 degrees apart. If the pre-image was reflected over the two intersecting lines, at what angle did they intersect? And second part is the rotation of the correlator is shown below what is the measure of x and y. Now let us start the solution of the given question. Now in the first part we are given that a pre-image and its image 232 degrees apart and then the pre-image was reflected over the two intersecting lines. We have to find the angle between the intersecting lines. Now we know that when a figure is reflected in two intersecting lines then final image is the rotation after figure about the point of intersection of the two lines and angle of rotation of the figure that is angle between the pre-image and image is twice the angle between the two intersecting lines. Now let angle of intersection be x degrees that is angle between the two intersecting lines is x degrees then of rotation is twice the angle between the two intersecting lines. So it will be 2 into x degrees. Now we are given that pre-image and its image are 232 degrees apart. So here we are given angle of rotation is equal to 232 degrees. Now where we have taken angle of rotation as 2x degrees x degrees that is angle of rotation is equal to 232 degrees. This implies x is equal to 232 degrees upon 2 which is equal to 116 degrees. Therefore angle between the intersects is 116 degrees and now let us start with second part. Now here we are given a quadrilateral abcd rotated at an angle of 150 degrees obtain its rotated image that is the quadrilateral a dash b dash c dash. Now in rotation the pre-image point and its corresponding image point are equidistant from center of rotation. Now let us name this center of rotation as o. Now here you can see the pre-image point d and its corresponding image point d dash are equidistant from center of rotation o. You can see the other points also. Of course the distance as well as the angle measure this will be equal to side bc is equal to side b dash c dash. Now bc is equal to this will be equal to b dash c dash which is 15 and this implies which implies upon 4 Now here as the two figures are congruent are equal it means angle b dash a dash d dash is equal to angle bad is equal to 80 degrees and this further implies upon 2 which is equal to 40 degrees. I is equal to 40 degrees to have the given question and that is all for this session. Hope you all have enjoyed this session.