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piyush_nitt
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Notation: < = angle
x = 180 - <TSU - <RSQ
x = 180 - (<TSU + <RSQ) … eqn 1
Statement 1: Without any restriction on <TSU, the value of x can vary. Insufficient.
Statement 2: Without any restriction on <RSQ, the value of x can vary. Insufficient.
Both statements together:
Triangles RQS and TUS are isosceles:
<RSQ = <RQS
<TUS = <TSU
Since triangle PRT is right angled, we have:
<UTS + <QRS = 90
180 - 2*(<TSU) + 180 - 2*(<RSQ) = 90
2*(<TSU + <RSQ) = 270
(<TSU + <RSQ) = 135 …eqn 2
Insert eqn 2 into eqn 1 to solve x. Sufficient.
Choose C.
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