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In the figure shown, the measure of angle PRS is how many de

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In the figure shown, the measure of angle PRS is how many de [#permalink] New post 31 Mar 2008, 04:43
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In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

(1) The measure of angle QPR is 30°.
(2) The sum of the measures of angles PQR and PRQ is 150°.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-attached-measure-of-angle-prs-is-how-many-102829.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Aug 2014, 06:33, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: In the figure shown, the measure of angle PRS is how many de [#permalink] New post 31 Mar 2008, 05:09
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tarek99 wrote:
In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees

(2) The sume of the measures of angles PQR and PRQ is 150 degrees






Can someone show me how to solve this problem? the OA is D, but how? I chose E.
thanks


<S is 90 degree, hope this is correct

PQR + QPS = 90 ---(1)
RPS + PRS = 90 ---(2)
both are because of internal angles of triangle = 180, and S is 90

What we want to find is PRS - PQR
we equate (1) and (2)
PQR + QPS = RPS + PRS
Thus PRS - PQR = QPS - RPS
so if we know difference between QPS and RPS, then we know the answer

1) QPR = 30
QPR = QPS - RPS = 30 - sufficient

2) tells that QPR = 30 from internal angles of triangle, thus sufficient

answer D
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Re: In the figure shown, the measure of angle PRS is how many de [#permalink] New post 31 Mar 2008, 05:35
thanks a lot man. and yes, you're right....angle S is 90 degrees. sorry for the typo!
thanks again
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Re: In the figure shown, the measure of angle PRS is how many de [#permalink] New post 10 Aug 2014, 10:26
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Re: In the figure shown, the measure of angle PRS is how many de [#permalink] New post 12 Aug 2014, 06:34
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In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

Image
Q: <PRS-<PQR=?

(1) The measure of angle QPR is 30°. <QPR=30 --> in triangle QPR three angles sum=180=<QPR+<PQR+<PRQ -->180=30+<PQR+(180-<PRS) --> 30=<PRS-<PQR SUFFICIENT

(2) The sum of the measures of angles PQR and PRQ is 150°. Basically the same information is given <PQR+<PRQ=150 --> <PQR+180-<PRS=150 --> 30=<PRS-<PQR SUFFICIENT

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-attached-measure-of-angle-prs-is-how-many-102829.html
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Re: In the figure shown, the measure of angle PRS is how many de   [#permalink] 12 Aug 2014, 06:34
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