Lines and Angles — MATHS STD 7 — Question

 
Construction: Draw a line $PQ$ parallel to $AB$ which is also parallel to $CD$
$\angle \text{QFC}+\angle \text{ECD}=180^\circ$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow \angle \text{QEC}+56^\circ=180^\circ$
$\Rightarrow \angle \text{QEC}=124^\circ$
Now, $\angle \text{BEQ}+\angle \text{QEC}=\angle \text{BEC}$
$\Rightarrow \angle \text{BEQ}+124^\circ=158^\circ$
$\Rightarrow\angle \text{BEQ}=34^\circ$
Now, $\angle \text{ABE}=\angle \text{BEQ}=34^\circ$ [Corresponding angles]
$\therefore \text{x}^\circ=34^\circ$
$\Rightarrow \text{x}=34$
Hence, the correct answer is option $(a).$