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805+ (Hard)|   Geometry|      
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Bunuel
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Line segments AB and CD intersect segment EF at points X and Y, respec 18 Sep 2018, 22:03
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Difficulty:

95% (hard)

Question Stats:

24% (02:02) correct 76% (01:55) wrong based on 53 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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E
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AnupamKT
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Line segments AB and CD intersect segment EF at points X and Y, respec 19 Sep 2018, 09:27
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Bunuel
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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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 2004 times ]

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fskilnik
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Line segments AB and CD intersect segment EF at points X and Y, respec 19 Sep 2018, 19:19
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Bunuel
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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\(? = \angle AXF\)

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.
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19Set18_2z.gif
19Set18_2z.gif [ 18.78 KiB | Viewed 1976 times ]

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