In the given figure , the value of x is

I can see how you might have trouble with this one, because the drawing isn't clear.
Here's what it's trying to show:

-- The line 'a'--'b' is the line where a wall meets the floor.

-- The line to 'c' is a vertical line drawn on the wall.

-- The line to 'd' is a line drawn on the floor.

If you can see it like that, then there are two giveaways for the value of 'x':

One way:
'c' is perpendicular to the floor.  That's the only way the angles
on the wall on each side of it ... 3x and 3x ... could be equal, and
they must be 90 degree angles, so 'x' is 30 degrees.    

The other way:
The line on the floor, to 'd', is not perpendicular to the wall, because the angles
on the floor on each side of it are not equal.  But the two of them do add up to
180 degrees, because the line 'a'--'b' is a straight line.
So 'x' is what's left over when 150 degrees is taken away from 180 degrees.
'x' is 30 degrees again.

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