Mathematics

# Mark the correct alternative of the following.In figure, AB$||$CD$||$EF, $\angle ABG=110^o$, $\angle GCD=100^o$ and $\angle BGC=x^o$. The value of x is?

$30$

##### SOLUTION
In figure $AB\ ||\ CD\ ||\ EF$
$\angle ABG=110^0, \angle GCD=100^0$
$\therefore \angle ABG$ and $\angle BGE$, $\angle GCD$ and $\angle CGF$ are pair of supplementary angles.

$\therefore \angle ABG+\angle BGE=180^0$
$\therefore 110^0+\angle BGE=180^0$
$\therefore \angle BGE=70^0$
Similarly,
$\therefore \angle GCD+\angle CGF=180^0$
$\therefore 100^0+\angle CGF=180^0$
$\therefore \angle CGF=80^0$

Now,
$\angle BGE+\angle BGC+\angle CGF=180^0$      ...$\{supplementary\ angles\}$
$\therefore 70^0+x+80^0=180^0$
$\therefore x+150^0=180^0$
$\therefore x=30^0$

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Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
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