 Hi and welcome to the session. Let us discuss the following question. Question says, consider the following parallelogram. Find the values of unknowns x, y and z. Let us now start with the solution. Now in given parallelogram A, B, C, D, angle B plus angle C is equal to 180 degrees since adjacent angles in our parallelogram are supplementary. So we can write in parallelogram A, B, C, D, angle B plus angle C is equal to 180 degrees. This is because adjacent angles in a parallelogram are supplementary. Now substituting corresponding values of angle B and angle C in this equation we get 100 degrees plus x is equal to 180 degrees. Clearly you can see in the figure that measure of angle B is 100 degrees and measure of angle C is x. Now to solve this equation for variable x we will subtract 100 degrees from both the sides of this equation and we get 100 degrees minus 100 degrees plus x is equal to 180 degrees minus 100 degrees. Now 100 degrees minus 100 degrees is 0. So we are left with x on left hand side is equal to sign is as it is and 180 degrees minus 100 degrees is 80 degrees. So value of x is 80 degrees. Now according to the property of the parallelogram opposite angles of a parallelogram are equal to each other. So we get angle D is equal to angle B and angle A is equal to angle C. This is because opposite angles of a parallelogram are equal. Now note that angle D is equal to y and angle B is equal to 100 degrees. So substituting corresponding values of angle D and angle B in this equality we get y is equal to 100 degrees and angle A is equal to z and angle C is equal to x which is further equal to 80 degrees. So substituting corresponding values of angle A and angle C in this equality we get z is equal to x is equal to 80 degrees. So we get z is equal to 80 degrees and y is equal to 100 degrees. So required value of x is 80 degrees. Required value of y is 100 degrees and required value of z is again 80 degrees. This is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.