Circle Geometry - How to find Central Angle

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I am currently having issue with this Circle Geometry Problem:

enter image description here

As noted in the picture, I know that the two triangle are similar. However, I am unable to find the other two angles.

Thanks for any help you can give!

Alex

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There are no parallel lines and so there are no similar triangles.

$y= 35^0$ (same angles in a circular segment)

and

$ x = 2 y = 2*35^0 =70^0$ (angle subtended at center is half that subtended at periphery.)