Meant to post this in data sufficiency, sorry.

Does look a little complicated but a fairly simple one. Explanation as follows.

(1)in triangle RSQ
qr=rs
So it follows that
angle rqs= angle rsq = y degrees (in a triangle, sides opposite congruent angles are equal)

Now, measure of angles qrs+rqs+rsq=180 (property of triangles)
qrs+y+y=180
qrs=180-2y.......(a)

Insufficient.

(2)in triangle STU
ST=TU
angle sut = angle tsu = z degrees (in a triangle, sides opposite congruent angles are equal)

similarly
measure of angles tsu+sut+stu=180 (property of triangles)
z+z+stu=180
stu=180-2z......(b)

Insufficient

Combining (1) and (2)

In triangle RPT

angle prt + angle rtp + angle rpt =180

180-2y+180-2z+90=180 (since angle qrs=angle prt, angle stu=angle rtp and from 1 and 2)
solving we get
y+z=135.....(c)

now,
angle rsq+angle qsu+angle tsu=180
y+x+z=180

x=180-(y+z)
x=180-135=45

Hence C. Hope this explanation helps.

Have added an image to clarify