Question

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

Answer 1

In trapezium $ABCD$,

$\angle A+\angle D={180}^{\circ }$[Adjacent angles]

$\Rightarrow 105+\angle D={180}^{\circ }$

$\Rightarrow \angle D={75}^{\circ }$

Steps for construction :

Step 1. Draw a line segment $AB=4cm$

Step 2. Draw a ray $\overrightarrow{AX}$ such that $\angle$ BAX = ${105}^{\circ }$

Step 3. Mark a point $D$ on $AX$ such that $AD=3cm$

Step 4. Draw $\overrightarrow{DX}$ such that $\angle ADY={75}^{\circ }$

Step 5. Mark a point $C$ such that $CD=8cm$

Step 6. Join $BC$

Hence , $ABCD$ is the required trapezium .