Mathematics

Mark the correct alternative of the following.
In figure, if AB, CD and EF are straight lines, then $$x=?$$


ANSWER

$$20$$


SOLUTION
Let the point of intersection of the lines AB, CD and EF  is O.
Then $$\angle AOE=\angle BOF=3x^o$$......(1) [ Opposite angles], $$\angle COF=\angle EOD=4x^o$$.....(2) and $$\angle BOD=\angle AOC=2x^o$$.....(3).
Then we've,
$$2(2x^o)+2(4x^o)+2(3x^o)=360^o$$ [ Since the sum of all the angles $$=360^o$$]
or, $$18x^0=360^o$$
or, $$x=20$$
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