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In the figure above, if PQRS is a parallelogram, then x =

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In the figure above, if PQRS is a parallelogram, then x = [#permalink] New post 24 Mar 2017, 14:30
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Bildschirmfoto 2017-03-24 um 23.28.47.png
Bildschirmfoto 2017-03-24 um 23.28.47.png [ 76.9 KiB | Viewed 869 times ]


In the figure above, if PQRS is a parallelogram,then x =

(A) 35
(B) 65
(C) 75
(D) 80
(E) 100
[Reveal] Spoiler: OA
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Re: In the figure above, if PQRS is a parallelogram, then x = [#permalink] New post 24 Mar 2017, 17:49
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Explanation

Now we have a parallelogram with sides PQ || RS and QS is transversal.

So \(\angle PQS = \angle QSR = 35\) as they are alternate interior angle.

And Finally

\(\angle PSQ + \angle QSR + 65 = 180\), as PS is a straight line.

\(\angle PSQ = 80\).

Hence option D is correct.
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Re: In the figure above, if PQRS is a parallelogram, then x = [#permalink] New post 10 May 2018, 06:43
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HarveyKlaus wrote:
Attachment:
Bildschirmfoto 2017-03-24 um 23.28.47.png


In the figure above, if PQRS is a parallelogram,then x =

(A) 35
(B) 65
(C) 75
(D) 80
(E) 100


We notice that QR and PS are parallel, and they are cut by the transversal QS. Using the property of alternate interior angles, we see that since angle PQS = 35 degrees, angle QSR must be 35 degrees also. Now notice that the three angles with vertex at point S add up to 180 degrees; therefore, we have:

x + 35 + 65 = 180

x + 100 = 180

x = 80 .

Answer: D
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Re: In the figure above, if PQRS is a parallelogram, then x =   [#permalink] 10 May 2018, 06:43
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