 Hi and welcome to the session. Let us discuss the following question. Question says, can a quadrilateral AVCD be a parallelogram if angle D plus angle B is equal to 180 degrees? Let us now start with the solution. Now we are given in the question, in quadrilateral AVCD, angle D plus angle B is equal to 180 degrees. Now first of all, let us draw a rough figure of quadrilateral AVCD. Now this figure represents quadrilateral AVCD such that sum of angle D and angle B is equal to 180 degrees. Now we have to find is, AVCD is a parallelogram. Now according to the property of a parallelogram, opposite angles of a parallelogram are equal to each other or we can say opposite angles of a parallelogram are of equal measure. Now the information given to us is not sufficient to decide if quadrilateral AVCD is a parallelogram. Quadrilateral AVCD can be a parallelogram only if angle B is equal to angle D is equal to 90 degrees. If both of these angles are right angles then AVCD is a parallelogram. Now if we take angle D and angle B equal to 90 degrees then AVCD is either a rectangle or it is a square. Clearly you can see angle D is equal to angle B and angle D plus angle B is equal to 180 degrees in both of these figures. So we can say if opposite angles are supplementary then quadrilateral AVCD may or may not be a parallelogram. Note that rectangle and square both satisfy all the properties of a parallelogram. So both of them represent a parallelogram. So we can write quadrilateral AVCD may or may not be a parallelogram. This is because opposite angles of a parallelogram are always equal or we can say opposite angles of a parallelogram are of equal measure and they may or may not be supplementary. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.