Question:
Construct a quadrilateral ABCD, where ∠A = 65°, ∠B = 105°, ∠C = 75° BC = 5.7 cm and CD = 6.8 cm.
Solution:
We know that the sum of all the angles in a quadrilateral is 360 .
i. e., $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}=360^{\circ}$
$\Rightarrow \angle \mathrm{D}=115^{\circ}$
Steps of Construction:
Step I : Draw BC $=5.7 \mathrm{~cm} .$
Step II : Construct $\angle \mathrm{XBC}=105^{\circ}$ at B and $\angle \mathrm{BCY}=105^{\circ}$ at C.
Step III : With C as the centre and radius $6.8 \mathrm{~cm}$, cut off CD $=6.8 \mathrm{~cm}$.
Step IV : At D, draw $\angle \mathrm{CDZ}=115^{\circ}$ such that it meets BY at A.
The quadrilateral so obtained is the required quadrilateral.