 Hi and welcome to the session. I am Asha and I am going to help you with the following position it says in figure 6.13 lines AB and CD intersect at the point O if angle AOC plus angle BOE is equal to 70 degree and angle BOE is equal to 40 degree find angle BOE and prefix angle COE. Let us now begin with the solution. First let us write what we are given. We are given two lines AB and CD intersecting at the point O. Also we are given the sum of angle AOC plus angle BOE is equal to 70 degree. So this is angle AOC and this is angle BOE and sum of these two angles is equal to 70 degree and also we are given that angle BOE is equal to 40 degree. This is angle BOE which is 40 degree. AB is the line BOE stands on it therefore sum of angles AOC BOE is equal to 180 degrees This is since they form a linear pair. Angle BOE can be written as sum of angles COE and BOE therefore this equation can further be written as AOC plus angle BOE plus angle COE is equal to 180 degree. Now sum of angles AOC and BOE is equal to 70 degree therefore on replacing the sum of these two angles by 70 degree we have 70 degree plus angle COE is equal to 180 degree which is further equal to angle COE is equal to 180 degree minus 70 degree. Further equal to 110 degree therefore angle COE is equal to 110 degree that is this angle is 110 degree. Now we have to find the reflex angle COE that is we have to find this angle. So what we will do is subtract 110 degree from 360 degree. So reflex angle COE is equal to 360 degree minus 110 degree which is equal to 250 degree. Thus reflex angle COE is equal to 250 degree. Now we need to find angle BOE this angle and since CD is a line OP stands on it therefore angle AOC and angle DOB form a linear pair. As the sum of these two angles is equal to 180 degree. Now angle BOC can be written as sum of angles DOE and angle COE plus then we have angle DOB is equal to 180 degree. Now this step is because angle BOC can be written as angle BOE plus angle COE. Now we have to find angle BOE so as it is angle COE is equal to 110 degree plus angle DOB is equal to 40 degree which is equal to 180 degree. Just further equal to angle BOE plus 110 plus 40 degree is equal to 150 degree which is equal to 180 degree and this implies angle BOE is equal to 180 degree minus 150 degree which is equal to 30 degree and thus angle BOE is equal to 30 degree. This angle is 30 degree. The answer answers are angle BOE is equal to 30 degree, reflex angle COE is equal to 250 degree. So this completes the solution hope you enjoyed it take care and bye for now.