Question

Construct a quadrilateral $PQRS$ with $PQ=7$ cm, $QR=6$ cm, $\angle P={45}^{\circ },\angle Q={60}^{\circ },\angle R={75}^{\circ }$.

Answer 1

First draw a line segment $QR=6$ cm.

Make angle ${60}^0$ at point $Q$ and angle ${75}^0$ at point $R$.

Open compass $7$ cm and mark curve at angle line from point $Q$.

This cut point is $P$.

Make angle ${45}^0$ at point $P$, this angle line cut the angle line at point $R$ at point $S$.

Join $S$ to $R$ and hence $PQRS$ is the required quadrilateral.