GRE Big book Test 7 question 12 (Section 2)

Any angle opposite the diameter is 90 degrees. So I was pretty certain that angle RTS = 90. I wasn’t sure of the measure of angle RXS but assumed that it is the same because angles away from the centre are usually considered equal. However, is there anything I’m missing? is it that because angle RXS is outside the circle it’ll be less than 90 degrees? If yes, can I get a reference video where I can review this again?

You need to clarify that further.

Sorry for the bad drawing but this is what I mean. However, angle RXS is out of the circle. So would love your thoughts on what I missed! :slight_smile:

That is the problem. One way to intuitively think about this is to take a point Y that is near X but is on the circle, and then draw \angle RYS. You know that is 90 degrees, which should give you a hint about what \angle RXS is.