 Hello students, let's work out the following problem. It says in figure 2, this is figure 2, AB is a diameter of a circle with center O, angle A, B, C is 70 degrees, angle C, A, D is 30 degrees, angle B, A, A is 60 degrees, find angle B, A, C, A, C, D and A, V, E. So we have to find angle B, A, C, that is this angle, then we have to find angle A, C, D, that is this angle and then we have to find angle A, V, E, that is this angle. Let's name this angle as 1, this as 2, this as 3, this as 4, this as 5, this as 6 and this as 7. So let's now start the solution. Now angle and also name this angle as 8, angle 8 is 90 degrees since it's an angle in semi-circle formed by the diameter AB. Now in triangle ABC, angle B is 70 degrees, angle C that is angle 8 is 90 degrees. Now we have to find angle B, A, C. Therefore, angle B, A, C that is angle 2 plus angle 3 plus angle 8 is 180 degrees as we know that sum of 3 angles in a triangle is 180 degrees. Now angle B is angle 3, so this implies angle 2 is equal to 180 minus angle 3 minus angle 8. Now angle 2 is equal to 180 degrees minus 70 degrees minus 90 degrees. So angle 2 is equal to 20 degrees, so this angle is 20 degrees. Now angle DAB is equal to angle 1 plus angle 2, angle 1 is 30 degrees, angle 2 is 20 degrees, so angle DAB is 50 degrees. Now ABCD is a cyclic quadrilateral, therefore sum of opposite angles will be 180 degrees that is angle DAB plus angle DCB is equal to 180 degrees. Now angle DAB is 50 degrees and angle DCB which is equal to angle 4 plus angle 8 equal to 180 degrees. So this implies angle 4 plus angle 8 is equal to 180 degrees minus 50 degrees that is 130 degrees. Now we have to find angle 4 that is angle ACD, so angle 4 is equal to 130 degrees minus angle 8 which is 70 degrees, so angle 4 is equal to 130 minus 70 degrees that is 60 degrees. Angle 8 is 90 degrees because it is an angle in semicircle, so this would be 130 minus 90 that is 40 degrees, so this angle is 40 degrees. Now again ACDE is a cyclic quadrilateral, therefore sum of opposite angles will be 180 degrees, therefore angle CAE plus angle CBE is equal to 180 degrees. Now we have to find angle ABE that is this angle. Now angle CAE is equal to angle 2 plus angle BAE and angle CBE is equal to angle CBA plus ABE and this is equal to 180 degrees. Now angle 2 is 20 degrees as we obtained above and angle BAE is given to be 60 degrees and angle CBA is given to be 70 degrees plus angle ABE and this is equal to 180 degrees, so this implies angle ABE is equal to 180 degrees minus 20 degrees minus 60 degrees minus 70 degrees, so this is equal to 30 degrees, so this angle is equal to 30 degrees. So we have obtained that angle BAC that is angle 2 is 20 degrees, angle ACD we have obtained it as 40 degrees and angle ABE we have obtained it as 30 degrees, so this completes the question and the session, by for now take care have a good day.