Since RQ = RS,
angle RQS = angle RSQ = a deg (assume) ---(1)
Similarly, since ST = TU,
angle TSU = angle TUS = b deg (assume) --- (2)
Then x = 180 - (a + b). Hence the question is to determine the value of (a+b)
Now consider eq(1) for triangle RQS, angle SRQ = 180 - 2a ----- (3)
from eq(2) for triangle STU, angle STU = 180 - 2b --------(4)
Now, consider the entire triangle RPT, where angle RPT = 90 with equantions (3) and (4)
Hence, 90 + 180 - 2a + 180 - 2b = 180. This will yeild, (a+b) = 135
Hence x = 180 - (a + b) = 180 - 135 = 45 degrees. Hence answer is [C]
GMAT Angles
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Source: Beat The GMAT — Data Sufficiency |
