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?


ANSWER

$$30$$


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
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