Question

Construct a quadrilateral PQRS in which PQ =4 cm, QR=5 cm, $\angle P={50}^{\circ },\angle Q={110}^{\circ }$ and $\angle R={70}^{\circ }$

Answer 1

steps of construction:
(i) Draw a line segment PQ =4 cm.
(ii) At P, draw a ray PX making an angle of ${50}^{\circ }$.
(iii) At Q, draw another ray QY making an angle of ${110}^{\circ }$ and cut off QR=5 cm.
(iv) At R, draw a ray RZ making an angle of ${70}^{\circ }$ which intersects PX at S.

Then PQRS is the required quadrilateral.