Question
Construct a quadrilateral $ABCD$ when $BC = 5.5\ cm, CD = 4.1\ cm$, $\angle\text{A}=70^\circ,\text{AB}=110^\circ$ and $\angle\text{D}=85^\circ.$
✓
Answer
We know that the sum of all the angles in a quadrilateral is $360$.
i.e.,$\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ$
$\Rightarrow\angle\text{C}=95^\circ$
Steps of construction:
Step $I$: Draw $BC = 5.5\ cm$.
Step $II$: Construct $\angle\text{XBC}=110^\circ$ at A and $\angle\text{BCY}=95^\circ$
Step $III$: With $C$ as the centre and radius $4.1\ cm$, cut off $CD = 4.1\ cm$.
Step $IV$: At $D$, draw $\angle\text{CDZ}=85^\circ$ such that it meets $BY$ at $A$.
The quadrilateral so obtained is the required quadrilateral.
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