Refer to the above image.
The red line is parallel to both AB and CD.
Hence,
- 1. (3x - 20) = y .......... Alternate angles
2. 180 - (5x + 55) = y .......... Alternate angles
Therefore, (3x - 20) + 180 - (5x + 55) = (3x + 15)
=> 5x = 90
=> x = 18
Geo 2
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Anurag@Gurome
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Refer to the above image.
The red line is parallel to both AB and CD.
Hence,
Therefore, (3x - 20) + 180 - (5x + 55) = (3x + 15)
=> 5x = 90
=> x = 18
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yellowho
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Does the red line cut that angle in half? ie. Does Y=Z?
[quote="Anurag@Gurome"][url=https://postimage.org/image/2rnxjc3gk/][img]https://s1.postimage.org/2rnxjc3gk/parl.jpg[/img][/url]
Refer to the above image.
The red line is parallel to both AB and CD.
Hence,
[list]1. (3x - 20) = y .......... Alternate angles
2. 180 - (5x + 55) = y .......... Alternate angles[/list]
Again (y + z) = (3x + 15)
Therefore, (3x - 20) + 180 - (5x + 55) = (3x + 15)
=> 5x = 90
=> x = 18[/quote]
[quote="Anurag@Gurome"][url=https://postimage.org/image/2rnxjc3gk/][img]https://s1.postimage.org/2rnxjc3gk/parl.jpg[/img][/url]
Refer to the above image.
The red line is parallel to both AB and CD.
Hence,
[list]1. (3x - 20) = y .......... Alternate angles
2. 180 - (5x + 55) = y .......... Alternate angles[/list]
Again (y + z) = (3x + 15)
Therefore, (3x - 20) + 180 - (5x + 55) = (3x + 15)
=> 5x = 90
=> x = 18[/quote]
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Anurag@Gurome
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Not necessarily.yellowho wrote:Does the red line cut that angle in half? ie. Does Y=Z?
In fact, if the figure is to scale, then they don't.
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GMATGuruNY
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The drawing above shows an alternate approach.
The sum of the angles inside the triangle whose base is on line CD must be 180.
(125-5x) + (165-3x) + (3x-20) = 180
270 - 5x = 180
-5x = -90
x = 18.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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yellowho
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Awesome! Love all your alternate approaches to problems Mitch. Can we come up with a new axiom: If Mitch can't come up with an alternate approach thats not math properties heavy, its not a good GMAT problem?
[quote="GMATGuruNY"][url=https://postimage.org/image/2ykbq5ll0/][img]https://s1.postimage.org/2ykbq5ll0/AB_parallel_CD.jpg[/img][/url]
The drawing above shows an alternate approach.
The sum of the angles inside the triangle whose base is on line CD must be 180.
(125-5x) + (165-3x) + (3x-20) = 180
270 - 5x = 180
-5x = -90
x = 18.[/quote]
[quote="GMATGuruNY"][url=https://postimage.org/image/2ykbq5ll0/][img]https://s1.postimage.org/2ykbq5ll0/AB_parallel_CD.jpg[/img][/url]
The drawing above shows an alternate approach.
The sum of the angles inside the triangle whose base is on line CD must be 180.
(125-5x) + (165-3x) + (3x-20) = 180
270 - 5x = 180
-5x = -90
x = 18.[/quote]
