Question

Using ruler and compasses only

construct a quadrilateral ABCD in whichAB = 4 cm BC = 7 cm angleA = angle C =105° and angle D= 60°

Answer 1

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Answer 2

Steps of construction:

(i) Draw a straight-line PQ, take a point A on it.

(ii) At A, construct ∠QAF = 60o

(iii) At A, draw AE ⊥ PQ from AE cut off AN = 3cm

(iv) Through N draw a straight line to PQ to meet AF at D.

(v) At D, draw AG ⊥ AD, from AG cut off AM = 4cm

(vi) Through M, draw at straight line parallel to AD to meet AQ in B and ND in C.

Then, ABCD is the required parallelogram