In Fig. AB || CD || EF, ABG=110^ , GCO=100^ and BGC=x^ . The value of x is:

In Fig. AB || CD || EF, ABG=110^ , GCO=100^ and BGC=x^ . The valu…

MCQ

In Fig. $AB || CD || EF, \angle \text{ABG}=110^\circ,\angle \text{GCO}=100^\circ$ and $\angle \text{BGC}=\text{x}^\circ.$ The value of $x$ is:

A
$35$
B
$50$
✓
$30$
D
$40$

✓

Answer

Correct option: C.

$30$

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 $(c).$