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

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Bunuel
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In the figure shown, AB || CD. x = ? [#permalink] New post   03 Sep 2021, 04:25
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In the figure shown, \(AB || CD. x =\) ?

A. 40
B. 70
C. 100
D. 110
E. 140

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BrentGMATPrepNow
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Re: In the figure shown, AB || CD. x = ? [#permalink] New post   03 Sep 2021, 07:34
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Bunuel wrote:

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

A. 40
B. 70
C. 100
D. 110
E. 140

Show Spoiler
Attachment:
1.jpg


To begin, let's remove the angle (x + 10) degrees and add a third line which is parallel to the other two lines:


Will now use the following properties when a transversal passes through parallel lines:


First, the angle here equals 80 degrees:


And the angle here equals 30 degrees:


So, the angle in question equals 110 degrees:


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

Answer: C
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IanStewart
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Re: In the figure shown, AB || CD. x = ? [#permalink] New post   03 Sep 2021, 07:43
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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.
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In the figure shown, AB || CD. x = ? [#permalink] New post   03 Sep 2021, 11:25
Bunuel wrote:

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



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
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Re: In the figure shown, AB || CD. x = ? [#permalink] New post   16 Nov 2022, 02:38
BrentGMATPrepNow wrote:
Bunuel wrote:

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

A. 40
B. 70
C. 100
D. 110
E. 140

Show Spoiler
Attachment:
1.jpg


To begin, let's remove the angle (x + 10) degrees and add a third line which is parallel to the other two lines:


Will now use the following properties when a transversal passes through parallel lines:


First, the angle here equals 80 degrees:


And the angle here equals 30 degrees:


So, the angle in question equals 110 degrees:


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

Answer: C


Hi BrentGMATPrepNow, is this added third line is parallel is due it's between the already two parallel lines? Thanks Brent
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BrentGMATPrepNow
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Re: In the figure shown, AB || CD. x = ? [#permalink] New post   16 Nov 2022, 08:04
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Kimberly77 wrote:
Hi BrentGMATPrepNow, is this added third line is parallel is due it's between the already two parallel lines? Thanks Brent


Here's how the parallel line properties are usually depicted:


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.
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Kimberly77
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Re: In the figure shown, AB || CD. x = ? [#permalink] New post   16 Nov 2022, 12:25
BrentGMATPrepNow wrote:
Kimberly77 wrote:
Hi BrentGMATPrepNow, is this added third line is parallel is due it's between the already two parallel lines? Thanks Brent


Here's how the parallel line properties are usually depicted:


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.


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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Re: In the figure shown, AB || CD. x = ? [#permalink]
16 Nov 2022, 12:25
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