Let's see how to construct a quadrilateral when three sides and two included angles are given.
Draw a quadrilateral \(PQRS\), where \(PQ = 7 \ cm\), \(QR = 8 \ cm\), \(RS = 6.5 \ cm\) and \(\angle Q = 75^\circ\) and \(\angle R = 100^\circ\).
Let us first draw the rough quadrilateral, which will help us to draw a fair quadrilateral.
Step 1: Draw a line segment \(QR = 8 \ cm\).
Step 2: Construct \(\angle RQX = 75^\circ\) using ruler and compass.
Step 3: With \(Q\) as centre and \(7 \ cm\) as radius, draw an arc, cutting \(QX\) at \(P\).
Step 4: Construct \(\angle QRY = 100^\circ\) using protractor.
Step 5: With \(R\) as centre and \(6.5 \ cm\) as radius, draw an arc cutting \(RY\) at \(S\). Now, join \(PS\). Thus, the quadrilateral \(PQRS\) is obtained.