I'm using the '<' notation to denote an angle.

<TSU + <RSQ + x = 180

1) <RQS = <RSQ

Lets say <QRS = a.
So <RQS = <RSQ = (180 - a)/2

We don't know the value of a and <TSU, hence insufficient.

2) <TSU = <TUS

Lets say <STU = b.
So <TSU = <TUS = (180 - b)/2

We don't know the value of b and <RSQ, hence insufficient.

Combining both statements:

<TSU + <RSQ + x = 180
(180-a)/2 + (180-b)/2 + x = 180 (Eqn 1)

And we know that a + b = 90 (Eqn 2)

Inserting equation 2 into equation 1:

(180 - (90 - b))/2 + (180 - b)/2 + x = 180
(90 + b + 180 - b)/2 + x = 180
270/2 + x = 180
x = 45. Sufficient.

Choose C.

-BM-

Thanks bluementor!!!