Question

Construction of quadrilaterals when two adjacent sides and three angles are given:
4. Construct a quadrilateral PQRS in which PQ = 4.5 cm $\angle PQR={120}^{\circ },QR=3.8cm,\angle QRS={100}^{\circ }$ and $\angle QPS={60}^{\circ }.$

Answer 1

First we draw a rough sketch of quadrilateral PQRS and write down its dimensions, as shown.(Rough Sketch) $\to$
Steps of Construction:

Step 1: Draw PQ = 4.5 cm.
Step 2: Make $\angle PQX={120}^{\circ }.$
Step 3: With Q as center and radius 3.8 cm, draw an arc, cutting QX at R. Join QR.
Step 4: Make $\angle QRY={100}^{\circ }.$
Step 5: $\angle QPZ={60}^{\circ }$ so that PZ and RY intersect each other at the point S.
Then, PQRS is the required quadrilateral.