Question

Construct a quadrilateral PQRS in which ∠P = 75°, ∠Q = 85°, ∠R = 110°, PQ = 4.1 cm. and QR = 3.9 cm.

Answer 1

First of all we draw a rough sketch of given measurements :

Steps of Construction

(i) First we draw a line segment PQ = 4.1 cm.

(ii) At point P, construct ∠QPX = 75° with PQ.

(iii) At point Q, construct ∠PQY = 85° with PQ and cut QR = 3.9 cm from QY.

(iv) At point R, construct ∠QRZ = 110° with QR intersecting PX at point S.

(v) Thus, we obtained a quadrilateral PQRS.