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answer E. both statements say the same thing , so its either D or E. given the info in either of the statemenst we cannot test the relationship between angles PRS and PQR. therefore answer E.

from ii, if Lpqr+Lprq =150,
Lqpr = 30, because Lprq+Lpqr+Lqpr =180 and 150+Lqpr =180. so again Lqpr =180-150= 30. therefore the angle prs is 30 degree greater than the angle pqr.

note: we dont need to find individual angle values, just the difference between angles PRS and PQR (lets call them x,y respectively), so we need to find x-y

let angle PRQ=z

statement I: angle QPR=30, so y+z=150, also z+x=180, therefore z=150-y, and 150-y+x=180 OR x-y=30. Sufficient.

Statement II: angles y+z=150, and we also know that z+x=180, so x-y=30, Sufficient.

Re: In the figure shown, the measure of angle PRS is how many [#permalink]

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09 Dec 2013, 14:04

I've just had a bit of a revelation in solving this problem.

Looking at triangle PRS we have the 90 degree angle at S and the two other angles adding up to 90. Now looking at the 30 degree angle of triangle PRQ. We know that PRS = 180 - PRQ but for the life of me I couldn't figure out why we knew the exact angle difference. Then it dawned on me, PRQ obviously has to add up to 180. Assuming angle PRQ remains constant, for every degree change in in QPR, there has to be an equal and opposite change in PQR. In other words, if QPR got 10 degrees larger, PQR would have to shrink by 10 degrees. If the line PQ were to be flat then obviously the "angle" measurement would be the same but it's 30 degrees "higher" meaning it's degree measure is 30 degrees less. If QPR changes, PQR must change by the same, but opposite amount.

It may not be anything special to the math geniuses here but it is to be :D

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

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

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