Question
Construct a quadrilateral $ABCD$ in which $AB = 5.6\ cm, BC = 4\ cm,$ $\angle\text{A}=50^\circ,\angle\text{B}=80^\circ$ and $\angle\text{D}=80^\circ.$
✓
Answer
Steps of construction:
Step 1: Draw $AB = 5.6\ cm.$
Step 2: Make $\angle\text{A}=50^\circ$ and $\angle\text{B}=105^\circ.$
Step 3: With $B$ as the centre, draw an arc of $4\ cm.$
Step 4: Sum of all the angles of the quadrilateral is $360^\circ .$
$\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ$
$50^\circ+105^\circ+\angle\text{C}+80^\circ=360^\circ$
$235^\circ+\angle\text{C}=360^\circ$
$\angle\text{C}=360^\circ-235^\circ$
$\angle\text{C}=125^\circ$
Step 5: With $C$ as the centre, make $\angle\text{C}$ equal to $\angle125^\circ.$
Step 6: Join $C$ and $D.$
Step 7: Measure $\angle\text{D}=80^\circ.$
Then, $ABCD$ is the required quadrilateral.
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