Need your thoughts on this

I'm getting C.

Made the diag and for simplicity marked angle UST as Z, angle RSQ as Y, angle RQS as L, angle SQP as M, angle SUT as A and angle SUP as B.

Whew!!

Now:

x+y+z = 180
(y+z) = 180 - x ...............1

stat 1 : Y = L; doesn't help me. Insuff.

stat 2: Z = A; doesn't help me. insuff.

Stat 1 & 2: Y = L and Z = A

L + M = 180
Since L = Y, Y + M = 180, M = 180 - Y .............. 2

A+B = 180
Since A = Z, Z + B = 180, B = 180 - Z ..............3

Further in quad. PQSU, x + M + angle QPU + B = 360

x = 270 - (M + B)
x = 270 - (180 - Y + 180 - Z) ........ (from 2 & 3)
x = 270 - [360 - (Y + Z)]
x = 270 - [360 - (180 - x)] .........(from 1)
x= 270 - [180 - x] = 90 - x
x = 45 degrees


Hopefully that is right

Whats the OA?