 Hello and welcome to the session. In this session we discuss the following question which says construct a trapezium PQRS in which PQ is equal to 6 cm, QR equal to 4 cm, RS equal to 3.2 cm, angle Q equal to 75 degrees and SR is parallel to PQ. Let's proceed with the construction. Before making the actual trapezium PQRS, first let's construct the rough sketch of the trapezium PQRS. This is the trapezium PQRS where we have PQ is equal to 6 cm, QR is equal to 4 cm, RS is equal to 3.2 cm, angle Q is 75 degrees and we have that SR is parallel to PQ. Now let's construct the trapezium PQRS step by step. First of all we draw PQ equal to 6 cm. We have drawn PQ equal to 6 cm. Now look at the rough sketch. As you can see angle Q is 75 degrees. So in the next step we make angle XQP equal to 75 degrees. This angle XQP is of measured 75 degrees. Now in the rough sketch as you can see we have QR of measured 4 cm. So in the next step with Q as the centre and radius 4 cm cut an arc on the ray XQ. So we have cut an arc of radius 4 cm taking Q as the centre. Let this point be point R. Now since it's given that SR is parallel to PQ so at point R we will draw SR parallel to PQ. So in the next step we write draw a ray RY parallel to PQ. To draw a ray RY parallel to PQ we make an angle of equal measure as angle Q at the point R. Now measuring this arc we cut an arc of equal measure on this arc. So we have drawn this arc which is of equal measure as this arc. Now from the point R we will pass a line which also passes through this arc. So this is the ray RY parallel to PQ since this angle is of measure 75 degrees that is angle XRY is of measure 75 degrees also angle XQP is of measure 75 degrees that is angle XRY is equal to angle XQP. Now since the corresponding angles are equal so this means that RY is parallel to PQ. Next we need to make RS equal to 3.2 cm so our next step would be with R as the centre and radius 3.2 cm an arc on the ray RY. So this is the arc of radius 3.2 cm from RS the centre take this point as point S then next we join so this PQ RS is the required trapezium where we have PQ equal to 6 cm angle Q equal to 75 degrees QR equal to 4 cm then RS equal to 3.2 cm. So this completes this session hope you have understood the solution for this question.