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Is AB parallel to CD?

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Is AB parallel to CD? [#permalink]

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New post 07 Feb 2018, 20:18
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Is AB parallel to CD?

(1) a + b = 180°

(2) a + c + d + e = 360°

[Reveal] Spoiler:
Attachment:
2018-02-08_0817.png
2018-02-08_0817.png [ 7.36 KiB | Viewed 255 times ]
[Reveal] Spoiler: OA

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Re: Is AB parallel to CD? [#permalink]

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New post 07 Feb 2018, 20:29
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Is AB parallel to CD?

(1) a + b = 180°
As a + b = 180° and b + d = 180(sum of angles in a straight line)
We can clearly say that a = d. Since the corresponding angles are equal,
we can say that AB is parallel to CD (Sufficient)

(2) a + c + d + e = 360°
d + e = 180° (Sum of angles in a straight line)
a + c + (d + e) = 360° -> a + c = 180°
Without knowing the individual angles, we cannot say AB is parallel
to CD (Insufficient) (Option A)
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Re: Is AB parallel to CD? [#permalink]

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New post 07 Feb 2018, 20:34
A is sufficient:If we assume line are parallel then 180-a=b implies if a+b = 180 it's parallel
B is not sufficient as we only conclude a = b but for parallel line we need a+b =180


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Re: Is AB parallel to CD?   [#permalink] 07 Feb 2018, 20:34
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