 Hi and welcome to the session. I am Arsha and I am going to help you with the following question which says, find the radian measure corresponding to the following degree measures. First let us learn the relation between radians and degree. First we have a circle, the center O, circle subtens at the center, an angle whose radian measure is 2 pi and its degree measure is 360 degree. Therefore it follows that 2 pi radian is equal to 360 degree or pi radian is equal to 180 degree. So with the help of this relation we are going to find the radian measures of the following degree measures. So this is our D idea. Let us now begin with the solution. Since we know pi radian is equal to 180 degree this implies that 1 degree is equal to pi upon 180 radian. Let us now begin with the first part where we have to find the radian measure of 25 degrees. Now since 1 degree is equal to pi upon 180 radian, so this implies 25 degrees is equal to 25 into pi upon 180 radian, pi pi is a 25 and 5 into 36 is 180. So we have pi pi upon 36 radian. Hence 25 degrees is equal to 5 pi upon 36 radians. So this implies the first part and now proceeding on to the second part where we have to find the radian measure of minus 47 degrees 30 minutes. Now since 1 degree is equal to pi upon 180 radian, therefore minus 47 degrees 30 minutes which can be written as minus 47 degree to 30 upon 60 degrees which is further equal to minus 47 1 by 2 which is further equal to minus 95 upon 2 degrees plus minus 95 upon 2 degrees is equal to minus 95 upon 2 into pi upon 180 radian which is equal to minus 95 pi upon 360 radian and on simplifying it we get minus 19 upon 72 which is further equal to minus 19 upon 72 pi radian and that is the radian measure of minus 47 degree and 30 minutes is minus 19 upon 72 pi. This completes the second part and now proceeding on to the third part where we have to find the radian measure of 240 degrees. Similarly since 1 degree is equal to pi upon 180 radian therefore 240 degrees is equal to 240 into pi upon 180 radian which is further equal to 240 upon 180 pi radian 0 cancels out with 0 and 6, 4 is 24, 6, 3 is 18. So we have 4 upon 3 pi radian thus the radian measure of 240 degrees is 4 upon 3 pi which completes the third part and now proceeding on to the fourth part where we have to find the radian measure of 520 degrees. Now since 1 degree is equal to pi upon 180 radian therefore 520 degrees is equal to 520 upon 180 pi radian which is further equal to 0 cancels out with 0 and we have 2 into 26 is 52 and 2 into minus 18 so 26 upon 9 pi radian and so the radian measure of 520 degrees is 26 upon 9 pi. This completes the last part and hence the session. Hope you enjoyed it. Take care and have a good day.