How do you work out the angle in this square? I have labelled all the angles that I can work out.



But I can't think of any other way to find the other angles without being 100% sure.

Thank you!



P.S. I have attached the official question - I have scribbled all over it with lines and therefore have drew out again by hand to make things clearer.
$\triangle PTS$ is isosceles because $PT =PS (= PQ) $. Hence $\angle PST = \frac{(180 - 30)}{2}=75^{\circ}$ and $\angle TSR = 90 - 75 = 15^{\circ}$. By symmetry $\triangle STR$ is isosceles so the required angle is $(180 - 30)=150^{\circ}$
Ok, This is the way I found. 


Construct a segment parallel to SR, with midpoint T. This creates 2 right triangles.
Extend ST or TR, creating an Isosceles triangle inside one of the new right triangles. 
Bisect the isosceles triangle into 2 congruent right triangles. You will note that both of them will be 30˚/60˚/90˚ triangles
This shows you that angle STR has two compliments of 30˚
Angle STR must be 120˚


Hope that helps!