Question

Is it possible to construct a unique quadrilateral ABCD with AB = 5 cm, BC = 6 cm, CD = 7 cm, $\angle ABC=$ ${40}^{\circ }$ and $\angle BCD=$ ${55}^{\circ }$?

• A. Yes, it is possible
• B. No, two such quadrilaterals can be constructed
• C. No, there can be infinite such quadrilaterals
• D. With the measure of an extra side, yes.

Answer 1

The correct option is A

Yes, it is possible

Step 1: Draw AB = 5 cm.

Step 2: At B, draw an angle of ${45}^{\circ }$ and mark 6 cm along that angle. Mark the point as C.

Step 3: At C, draw an angle of ${55}^{\circ }$ and mark 7 cm along that angle. Mark the point as D.

Step 4: Join points A and D. So, quadrilateral ABCD can be constructed.