First of all we draw a rough sketch of given measurements :
We know that sum of all angles of a quadrilateral = 360°
∴ ∠D + ∠N + ∠S + ∠I= 360°
∴ ∠D = 360° – (120° + 90° + 60°)
= 360° – 270° = 90*
∴ ∠D = 90°
Steps of Construction
(i) First of all draw a line segment NS = 3.7 cm.
(ii) At point N and S construct ∠SNX = 120° and ∠NSY = 90° with N.S respectively.
(iii) Cut DN = 2.5 cm from NX.
(iv) At point D, construct ∠NDZ = 90° with DN and intersecting SY at I.
Thus, we obtained required quadrilateral DNSI
