Question
Construct a quadrilateral ABCD, where AB = 5.5cm, BC = 3.7cm, $\angle\text{A}=60^\circ,$ $\angle\text{B}=105^\circ$ and $\angle\text{D}=90^\circ$
✓
Answer
We know that the sum of all the angles in a quadrilateral is 360.i.e., $\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ$
$\Rightarrow\angle\text{C}=105^\circ$
Steps of construction:
Step I: Draw AB = 5.5cm.
Step II: Construct $\angle\text{XAB}=60^\circ$ at A and $\angle\text{ABY}=105^\circ.$
Step III: With B as the centre and radius 3.7cm, cut off BC = 3.7cm.
Step IV: At C, draw $\angle\text{BCZ}=105^\circ$ such that it meets AX at D.
The quadrilateral so obtained is the required quadrilateral.
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