Question

Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4 cm, ∠A = 50°, ∠B = 105° and ∠D = 80°.

Answer 1

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