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

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Math Expert
Joined: 02 Sep 2009
Posts: 54440
In the above figure, if L1 is parallel to L2 , what is the value of x  [#permalink]

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01 Aug 2017, 05:05
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Difficulty:

35% (medium)

Question Stats:

52% (00:43) correct 48% (00:37) wrong based on 65 sessions

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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

Attachment:

2017-08-01_1351.png [ 3.85 KiB | Viewed 2688 times ]

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

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06 Aug 2017, 12:38
Bunuel wrote:

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

Attachment:
2017-08-01_1351.png

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

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

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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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