Question

Construct a parallelogram PQRS where the $\angle Q=120°$, PR is the diagonal, $\angle RPQ=30°$.

• A. We cannot construct the quadrilateral PQRS.
• B.
• C. Data insufficient
• D.

Answer 1

The correct option is B

Since PQRS is a parallelogram, the opposite sides are equal.

Steps of construction:

Step 1: Draw a line segment of length 6 cm.

Step 2: At the point Q, construct an angle 120° and at point P construct an angle of 30° and extend the lines.

Step 3: Let the intersection of the extended lines be R.

Step 4: With center P and radius QR and with centre R and radius PQ, draw arcs intersecting each other at S.

Step 5: Join S to P and R.

The following figure shows the required quadrilateral.