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# Triangle ABC

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Triangle ABC [#permalink]  18 Mar 2018, 10:12
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Question Stats:

91% (00:33) correct 8% (02:44) wrong based on 12 sessions
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triangle_l_m.jpg [ 10.33 KiB | Viewed 316 times ]

$$\Delta ABC$$ is equilateral. Line $$l$$ is parallel to side $$BC$$ and line $$m$$ is parallel to side $$AC$$.

 Quantity A Quantity B $$x$$ $$60$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Triangle ABC [#permalink]  02 Apr 2018, 19:37
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METHOD ONE:

If any 2 lines are parallel, they must form the same slope if they were in the xy coordinate plane. So we can see that lines l and m are forming the same slopes as the two sides on the right and bottom of the equilateral triangle. So we can see that whatever angle l and m form with each other, must be the same as the angle that the lower right hand angle in the equilateral triangle is forming. Since equilateral triangles only have 60° angles, x must be 60°, so the answer is C.

METHOD TWO:

Imagination! If we imagine that we sort of slide lines l and m together directly upwards, eventually line m will be exactly overlapping with line AC. Then if we imagine that we scroll lines l and m to the left, eventually they will perfectly overlap the lower right hand corner of the equilateral triangle. Since this angle must be 60°, so must x, so the answer must be C.
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Re: Triangle ABC   [#permalink] 02 Apr 2018, 19:37
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# Triangle ABC

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