I can't tell what the question is.
Where is the 52 degree angle?
Where is the 196 degree angle?
If the measure of an arc is 52º then the corresponding central angle is 52º also.
btw, angle SRT = 124º
An arc has a length it does not have an angle.
However it does subtend an angle at the centre and yes, I assume that arc DU subtends an angle of 52 degrees at the centre.
What has 196 degrees got to do with anything?
Without this being clarified, I angle SRT does not have a specific value.
Here are two of the infinite number of possible solutions.
Alan has just told me that he thinks 196 degrees is the angle that major arc ST subtends at the center.
That makes sense.
So this is the graphical solution: Yes I agree that angle SRT=124 degrees.
(This is not a logic solution though)