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# In the figure above, if PQ is parallel to RS, then x =

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Math Expert
Joined: 02 Sep 2009
Posts: 55236
In the figure above, if PQ is parallel to RS, then x =  [#permalink]

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01 Aug 2017, 09:44
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In the figure above, if PQ is parallel to RS, then x =

(A) 90
(B) 80
(C) 70
(D) 60
(E) 40

Attachment:

2017-08-01_2039_002.png [ 8.36 KiB | Viewed 7624 times ]

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Re: In the figure above, if PQ is parallel to RS, then x =  [#permalink]

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01 Aug 2017, 09:54
Quote:

If we extend RP further down, lets call the extended line PT.
Now, as PQ is parallel to RS, Angle QPT is also 120 degree(corresponding angles)

Since the sum of angles in a straight line is 180 degree,
x + 20 + QPT = 180
x = 180 - 20 - 120 = 40(Option E)
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Re: In the figure above, if PQ is parallel to RS, then x =  [#permalink]

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01 Aug 2017, 10:10
Bunuel wrote:

In the figure above, if PQ is parallel to RS, then x =

(A) 90
(B) 80
(C) 70
(D) 60
(E) 40

Attachment:
2017-08-01_2039_002.png

As PQ is parallel to RS angle
RPQ +PRS= 180
so RPQ=60

hence X=40
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Re: In the figure above, if PQ is parallel to RS, then x =  [#permalink]

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01 Aug 2017, 11:32
Let's extend line RP and call the point on the bottom T. Since PQ is parallel to RS and line RP cuts through these parallel lines. Angle TPQ is also 120.

Now we know that 120+20+x=180 => x = 40
Re: In the figure above, if PQ is parallel to RS, then x =   [#permalink] 01 Aug 2017, 11:32
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