Doubt I Geometry concept clarification

GRE Quant Problem Solving
1

Hi! Wanted to check my understanding of the central angle theorem with you:

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In this problem, I made the deduction that XCY = 60 because XYZ = 30 degree. Is my application of the central angle theorem correct here?

I revisited Prepswift video on this, there it just said that in cases of a polygon, we can onyl deduce the following:

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So I wasn’t really sure of (1) what does this really mean? and (2) If my understanding is okay

Would be great if you could help me here, thanks!

2

Did you mean \angle XZY = 30^{\circ}? If so, then yes you’re right

3

Yes! Thanks