Mark ( ) against the correct answer.In the given figure, AB , =110^ ,, =100^ and BCG=x^ Then, x= ?

Mark ( ) against the correct answer.In the given figure, AB , =11…

MCQ

Mark $(\checkmark)$ against the correct answer.In the given figure, $\text{AB}\parallel\text{CD}\parallel\text{EF},\angle\text{ABG}=110^\circ,$, $\angle\text{GCD}=100^\circ$ and $\text{BCG}=\text{x}^\circ$ Then, $\text{x}={}?$

A
$35$
B
$50$
✓
$30$
D
$40$

✓

Answer

Correct option: C.

$30$

In the figure,
$\text{PQ}\parallel\text{RS}\parallel\text{EF}$
$\angle\text{ABG}=110^\circ$ and $\angle\text{GCD}=100^\circ$
$\angle\text{BGC}=\text{x}^\circ$
$\text{AB}\parallel\text{EF}$
$\angle\text{ABG}+\angle\text{BGE}=180^\circ$
$\Rightarrow110^\circ+\angle\text{BGE}=180^\circ$
$\Rightarrow\angle\text{BGE}=180^\circ-110^\circ=70^\circ$
Similarly $\text{CD}\parallel\text{EF}$
$\angle\text{GCD}+\angle\text{CGF}=180^\circ$
$\Rightarrow100^\circ+\angle\text{CGF}=180^\circ$
But $\angle\text{BGE}+\angle\text{BGC}+\angle\text{CGF}=180^\circ$
$\Rightarrow70^\circ+\text{x}+80^\circ=180^\circ$
$\Rightarrow\text{x}=180^\circ-150^\circ=30^\circ$