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