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