Question

Construct a quadrilateral ABCD, where ∠A = 65°, ∠B = 105°, ∠C = 75° BC = 5.7 cm and CD = 6.8 cm.

Answer 1

\[\text { We know that the sum of all the angles in a quadrilateral is 360 } . \]

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

\[ \Rightarrow \angle D = 115^\circ\]

Steps of Construction: 

Step I: Draw BC = 5 . 7 cm . 

\[\text { Step II: Construct } \angle XBC = 105^\circ\text {  at B and } \angle BCY = 105^\circ at C . \]

Step III : With C as the centre and radius 6 . 8 cm, cut off CD = 6 . 8 cm . 

\[\text { Step IV: At D, draw } \angle CDZ = 115^\circ  \text { such that it meets BY at A } . \]

The quadrilateral so obtained is the required quadrilateral .