The biggest difficulty that one may face on this question is to stop oneself from thinking about complex ideas to solve the question. Once we get to the answer, you will realize that even 700 level questions on the GMAT test basic concepts very often.
From the diagram, we recognize that triangle PRT is a right-angled triangle, right-angled at P. Therefore, angles R and T should add up to 90 degrees.
From statement I alone, length of QR = length of RS. Therefore, angle RQS = angle RSQ = y (say)
There is no information about the other angles or the other line segments. Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, length of ST = length of TU. Therefore, angle TSU = angle TUS = z (say).
There is no information about the other angles or the other line segments. Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we have the following:
From statement I alone, angle RQS = angle RSQ = y. Therefore, angle QRS = 180 – 2y (from the interior angle property of a triangle).
From statement II alone, angle TSU = angle TUS = z. Therefore, angle STU = 180 – 2z (from the interior angle property of a triangle).
IN triangle PRT, angle PRT + angle PTR = 90 degrees (angle TPR = 90 degrees).
Since angle PRT = angle QRS and angle PTR = angle STU, we can substitute the magnitudes of these angles in the equation above.
Therefore, 180 – 2y + 180 – 2z = 90. Simplifying, we obtain y+z = 135.
In the given diagram, angle RSQ + angle QSU + angle TSU = 180 (linearly adjacent angles add up to 180 degrees)
Substituting the values, we have y + x + z = 180. Since y + z = 135, x = 45 degrees.
The combination of statements is sufficient to answer the question. Answer option E can be eliminated.
The correct answer option is C.
If the diagram appears complex, it is not necessary that the solution should consist of complex concepts. That's the learning from this 700 level Geometry question.
Hope that helps!
Aravind B T
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