Lines and Angles — Maths STD 7 — Question

Since, $AB \| EG$
$\therefore \angle \text{ABG}+\angle \text{EGB}=180^\circ ($Angles on the same side of a transversal line are supplementary$)$
$\Rightarrow 110^\circ+\angle \text{EGB}=180^\circ$
$\Rightarrow \angle \text{EGB}=70^\circ$
Again, $CD \| GF$
$\therefore \angle \text{DCG}+\angle \text{FGC}=180^\circ ($Angles on the same side of a transversal line are supplementary$)$
$\Rightarrow 100^\circ+\angle \text{FGC}=180^\circ$
$\Rightarrow \angle \text{FGC}=80^\circ$
Now, $\angle \text{EGB}+\angle \text{BGC}+\angle \text{FGC}=180^\circ$
$\Rightarrow 70^\circ+\text{x}^\circ+80^\circ=180^\circ$
$\Rightarrow 150^\circ+ \text{x}^\circ=180^\circ$
$\Rightarrow \text{x}^\circ=30^\circ$
$\Rightarrow \text{x}=30$
Hence, the correct answer is option $(c).$