Question

Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.

Answer 1

We know that the sum of all the angles in a quadrilateral is 360 . 

\[i . e . , \angle A + \angle B + \angle C + \angle D = 360^\circ\]

\[ \Rightarrow \angle C = 95^\circ\]

Steps of construction: 

Step I: Draw BC = 5 . 5 cm . 

\[\text { Step II: Construct } \angle XBC = 110^\circ\text {  at A and }\angle BCY = 95^\circ . \]

Step III: With C as the centre and radius 4 . 1 cm, cut off CD = 4 . 1 cm . 

\[\text { Step IV: At D, draw } \angle CDZ = 85^\circ \text {P such that it meets BY at A } . \]

The quadrilateral so obtained is the required quadrilateral .