I'm hoping that someone can give me some help with the following problem:

O is the centre of the circle (show on the attachment to this post) and AB is parallel to CD. Find the angles labelled x and y.

With a bit of cheating I was able to find that x = 32^{o}and y = 58^{o}but my questions is 'why' or what is the 'proof' of this?

Many Thanks.