Question

Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, ∠P = ∠R = 100° and ∠S = 75°.

Answer 1

Steps of construction:
Step 1: Draw PQ= $5cm$
Step 2:
$$\begin{gathered} \angle P+\angle Q+\angle R+\angle S={360}^{\circ } \\ {100}^{\circ }+\angle Q+{100}^{\circ }+{75}^{\circ }={360}^{\circ } \\ {275}^{\circ }+\angle Q={360}^{\circ } \\ \angle Q={360}^{\circ }-{275}^{\circ } \\ \angle Q={85}^{\circ } \end{gathered}$$
Step 3: Make $\angle P={100}^{\circ }and\angle Q={85}^{\circ }$
Step 3: With Q as the centre, draw an arc of $6.5cm$.
Step 4: Make $\angle R={100}^{\circ }$
Step 6: Join R and S.
Step 7: Measure $\angle S={75}^{\circ }$
Then, $PQRS$ is the required quadrilateral.