In the figure shown, AB || CD. x = ?

Question

https://gmatclub.com/forum/download/file.php?id=63516 In the figure shown, AB || CD. x = ? A. 40 B. 70 C. 100 D. 110 E. 140 1.jpg

BrentGMATPrepNow · Accepted Answer

To begin, let's remove the angle (x + 10) degrees and add a third line which is parallel to the other two lines:
 https://i.imgur.com/feQ4u89.png

Will now use the following properties when a transversal passes through parallel lines:
 https://i.imgur.com/0bErMsT.png

First, the angle here equals   80   degrees:
 https://i.imgur.com/nm8Npyo.png

And the angle here equals   30   degrees:
 https://i.imgur.com/C3d5HlN.png

So, the angle in question equals   110   degrees:
 https://i.imgur.com/l0F9DTI.png

This means we can write: x + 10 =   110  , which means x = 100

Answer: C

IanStewart · Answer

The angle on the other side of the 30 degree angle is 150 degrees. Now if you draw a vertical line from point B to point D, you get a pentagon. That vertical line creates two 90 degree angles in the pentagon, and we know the three other angles in the pentagon are 150, 100, and x+10. Since the angles in a pentagon add to 540, we have 440 + x = 540 and x = 100.

Crytiocanalyst · Answer

supplemetary angle to 100 equals 80 since AB is a straight line 
let a line extending from CD to AB and let us name it E then OEB =30 parallel lines

in triangle OEB angle EOB = 180 -80-30 = 70 
Since OEB and BOD is supplementary then x= 180 - 70-10 = 100

Therefore IMO C

Kimberly77 · Answer

Hi  BrentGMATPrepNow , is this added third line is parallel is due it's between the already two parallel lines? Thanks Brent

BrentGMATPrepNow · Answer

Here's how the parallel line properties are usually depicted: 
 https://i.imgur.com/0bErMsT.png

Since the original diagram doesn't look like this, we can't YET apply those properties. 
However, if we add a third line (as I have done), we can apply those properties.

Kimberly77 · Answer

Thanks  BrentGMATPrepNow . I see what you mean since the added line is between the two parallel lines therefore we can apply the line properties.

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In the figure shown, AB || CD. x = ?

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In the figure shown, AB || CD. x = ?

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