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

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
Line segments AB and CD intersect segment EF at points X and Y, respec  [#permalink]

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18 Sep 2018, 21:03
00:00

Difficulty:

95% (hard)

Question Stats:

21% (02:01) correct 79% (01:59) wrong based on 39 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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Joined: 13 Mar 2018
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Re: Line segments AB and CD intersect segment EF at points X and Y, respec  [#permalink]

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19 Sep 2018, 08:27
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°.

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.

Attachments

IMG_20180919_215433.jpg [ 321.26 KiB | Viewed 267 times ]

GMATH Teacher
Status: GMATH founder
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Posts: 629
Re: Line segments AB and CD intersect segment EF at points X and Y, respec  [#permalink]

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19 Sep 2018, 18:19
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 [ 18.78 KiB | Viewed 236 times ]

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Re: Line segments AB and CD intersect segment EF at points X and Y, respec &nbs [#permalink] 19 Sep 2018, 18:19
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