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In the above figure, if L1 is parallel to L2 , what is the value of x

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V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124659 [0], given: 12079

In the above figure, if L1 is parallel to L2 , what is the value of x [#permalink]

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New post 01 Aug 2017, 05:05
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A
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C
D
E

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Question Stats:

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In the above figure, if L1 is parallel to L2, what is the value of x in terms of a?

(A) 180 – a
(B) 180 + a
(C) 270 – a
(D) 360 + a
(E) 360 – a

[Reveal] Spoiler:
Attachment:
2017-08-01_1351.png
2017-08-01_1351.png [ 3.85 KiB | Viewed 440 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 124659 [0], given: 12079

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G
Joined: 22 May 2016
Posts: 655

Kudos [?]: 191 [0], given: 499

In the above figure, if L1 is parallel to L2 , what is the value of x [#permalink]

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New post 06 Aug 2017, 12:38
Bunuel wrote:
Image
In the above figure, if L1 is parallel to L2, what is the value of x in terms of a?

(A) 180 – a
(B) 180 + a
(C) 270 – a
(D) 360 + a
(E) 360 – a

[Reveal] Spoiler:
Attachment:
2017-08-01_1351.png

Shorter answer: Angles around a point always sum to 360°
x + a = 360
x = 360 - a

Answer E

Longer answer: Extend L2 to the right.

L1 and L2 are parallel lines (given) cut by a traversal. Alternate interior angle measures are equal.

Where L2 and the transversal meet (a point around which there are 360°) there is an alternate interior angle that = a:

\(_{L2}\)________a/

And x is the measure of the portion of the 360° that does not include a, i.e., all the degrees below L2 and to the right of the transversal:

\(_{L2}\)_________/\(_{x}\)

x + a = 360
x = 360 - a

Answer E

Kudos [?]: 191 [0], given: 499

In the above figure, if L1 is parallel to L2 , what is the value of x   [#permalink] 06 Aug 2017, 12:38
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In the above figure, if L1 is parallel to L2 , what is the value of x

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