Question

Construction of quadrilaterals when three sides and two included angles are given:
3. Construct a quadrilateral ABCD in which $AB=3.6cm,\angle ABC={80}^{\circ },BC=4cm,\angle BAD={120}^{\circ }$ and AD = 5 cm.

Answer 1

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

Step 1: Draw AB = 3.6 cm.
Step 2: Make $\angle ABX={80}^{\circ }.$
Step 3: With B as center and radius equal to 4 cm, draw an arc, cutting BX at C.
Step 4: Make $\angle BAY={120}^{\circ }.$
Step 5: With A as center and 5 cm as radius, draw an arc, cutting AY at D. Step 6: Join CD.
Then, ABCD is the required quadrilateral.