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Line segments AB and CD intersect segment EF at points X and Y, respec

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Line segments AB and CD intersect segment EF at points X and Y, respec  [#permalink]

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New post 18 Sep 2018, 22:03
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

21% (01:59) correct 79% (01:56) wrong based on 34 sessions

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Line segments AB and CD intersect segment EF at points X and Y, respectively. What is the measure of angle AXF?

(1) Angle CYF is 120°.
(2) Angle AXY is 30°.

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Re: Line segments AB and CD intersect segment EF at points X and Y, respec  [#permalink]

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New post 19 Sep 2018, 09:27
Bunuel wrote:
Line segments AB and CD intersect segment EF at points X and Y, respectively. What is the measure of angle AXF?

(1) Angle CYF is 120°.
(2) Angle AXY is 30°.



Answer will be " B"

Refer attached picture:

From statement 1: Given Angle CYF is 120°, with this we cannot find angle AXF as it is not mentioned whether line AB & CD is parallel or not. Hence insufficient.

From statement 2: Angle AXY is 30°. From the attached picture, angle AXY=angle AXF=30 degree. So sufficient.

Hence answer is "B"

Please advice.
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IMG_20180919_215433.jpg
IMG_20180919_215433.jpg [ 321.26 KiB | Viewed 212 times ]

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Re: Line segments AB and CD intersect segment EF at points X and Y, respec  [#permalink]

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New post 19 Sep 2018, 19:19
Bunuel wrote:
Line segments AB and CD intersect segment EF at points X and Y, respectively. What is the measure of angle AXF?

(1) Angle CYF is 120°.
(2) Angle AXY is 30°.

\(? = \angle AXF\)

Without loss of generality we may assume line segment EF is contained in a horizontal line.

We went immediately to (1+2), because our GEOMETRIC BIFURCATION proves the right answer is (E).

Please see image attached, in which we have two different numerical values for our FOCUS:

> Angle AXF may be equal to 30 degrees.
> Angle AXF may be equal to 150 degrees (the supplement of 30 degrees).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
Attachments

19Set18_2z.gif
19Set18_2z.gif [ 18.78 KiB | Viewed 181 times ]


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Re: Line segments AB and CD intersect segment EF at points X and Y, respec &nbs [#permalink] 19 Sep 2018, 19:19
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