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I got this question right, but just by thinking about the relationships of the different points on the triangle. Afterwards, I did this mathematically, and it took me a very long time with a large system of equations. Anyone have any thoughts on a quicker but mathematical way of doing this?
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17 Aug 2008, 09:14
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Unsure if my solution is right, give your thoughts.
Angle R + Angle T = Angle P = 90 degrees.
Angle R + 2A = 180 degrees (2A because QR = RS)
Angle T + 2B = 180 degrees (2B because ST = TU)
Angle R + 2A + Angle T + 2B = 360 degrees (1 triangle = 180 degrees)
90 degrees + 2A + 2B = 360 degrees
2A + 2B = 270 degrees
A + x + B = 180 degrees (given it's a straight line on the triangle)
Simplify 2A + 2B = 270 degrees by dividing by 2, which results: A + B = 135 degrees.
A + B + x = 180 degrees
135 degrees + x = 180 degrees
x = 45 degrees regardless what value A and B are as long as the given conditions are met.
Therefore, an answer can be found when both conditions are met.
Angle R + Angle T = Angle P = 90 degrees.
Angle R + 2A = 180 degrees (2A because QR = RS)
Angle T + 2B = 180 degrees (2B because ST = TU)
Angle R + 2A + Angle T + 2B = 360 degrees (1 triangle = 180 degrees)
90 degrees + 2A + 2B = 360 degrees
2A + 2B = 270 degrees
A + x + B = 180 degrees (given it's a straight line on the triangle)
Simplify 2A + 2B = 270 degrees by dividing by 2, which results: A + B = 135 degrees.
A + B + x = 180 degrees
135 degrees + x = 180 degrees
x = 45 degrees regardless what value A and B are as long as the given conditions are met.
Therefore, an answer can be found when both conditions are met.
17 Aug 2008, 09:15
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C.
Say angle PTR=x. Then angle PRT= 90-x (for right triangle PRT)
1) triangle QRS is isoceles. so angle rsq = angle rqs = (180-(90-x))/2 = 90/2 + x/2
Insufficient. for dtermining x as angle tsu is still unknown.
2) similarly will give you tus=tsu = (180-x)/2 = 180/2-x/2
Insufficient as with this alone rsq is unknown
Combine to get x= 180-rsq-tsu
So C
Say angle PTR=x. Then angle PRT= 90-x (for right triangle PRT)
1) triangle QRS is isoceles. so angle rsq = angle rqs = (180-(90-x))/2 = 90/2 + x/2
Insufficient. for dtermining x as angle tsu is still unknown.
2) similarly will give you tus=tsu = (180-x)/2 = 180/2-x/2
Insufficient as with this alone rsq is unknown
Combine to get x= 180-rsq-tsu
So C
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
