Data Sufficiency

How do I solve this? Thanks in advance.

atarafder wrote:How do I solve this? Thanks in advance.

Let angle RSQ = y and angle UST = z

We have x + y + z = 180

1 - insufficient. In triangle RQS, 2y + angle-QRS = 180

2 - insufficient. In triangle STU, 2z + angle-UTS = 180

Combining and adding both,

2y + angle-QRS + 2z + angle-UTS = 360

We know angle-QRS + angle-UTS = 90 degrees (if you take triangle
PRT, one angle is 90 degrees)

2y + 2z = 360 - 90
y + z = 135

We also have x + y + z = 180 (straight line).

So we can compute x.

Hence C

Thank you.