Question

Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, $\angle N={60}^{\circ },\angle E={110}^{\circ }$ and $\angle S={85}^{\circ }$.

Answer 1

Fourth angle $={360}^{\circ }-({60}^{\circ }+{110}^{\circ }+{85}^{\circ })={360}^{\circ }-{255}^{\circ }={105}^{\circ }$
Steps of Construction
Step I: Draw NE = 7 cm.
Step II: Make $\angle NEX={110}^{\circ }$.
Step III: With E as centre and radius 6 cm, draw an arc, cutting EX at W.
Step IV: Make $\angle EWY={105}^{\circ }$.
Step V: Make $\angle ENZ={60}^{\circ }$, so that NZ and WY intersect each other at point S.
Thus, NEWS is the required quadrilateral.