Construct a quadrilateral PQRS where PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.
We know that the sum of all the angles in a quadrilateral is 360.
i.e., ∠P+∠Q+∠R+∠S = 360°
∠ Q = 75°
Steps of construction:
Step I: Draw PQ = 3.5 cm.
Step II: Construct ∠XPQ = 75° and ∠PQY = 75°.
Step III: With Q as the center and radius 6.5 cm, cut off QR = 6.5
Step IV: At R, draw ∠QRZ = 105° such that it meets PX at S.