Question

Question 186
Construct a trapezium ABCD in which $AB\parallel DC,\angle A={105}^{\circ }$, AD = 3 cm, AB = 4 cm and CD = 8 cm.

Answer 1

We know that.
$\angle A+\angle D=180$ [$\because$ sum of adjacent angle of a trapezium is ${180}^{\circ }$]
${105}^{\circ }+\angle D={180}^{\circ }$
$\angle D={75}^{\circ }$

Steps of Construction
Step I Draw AB = 4 cm.
Step II Draw $\overline{AX}$ such that $\angle BAX={105}^{\circ }$.
Step III Mark a point D on AX such that AD = 3 cm.
Step IV Draw $\overline{DY}$ such that $\angle ADY={75}^{\circ }$.
Step V Mark a point C such that CD = 8 cm.
Step VI Join BC.
Hence, ABCD is the required trapezium.